messages listlengths 3 3 | topic stringclasses 1
value | subtopic stringclasses 18
values |
|---|---|---|
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{2964}{2964}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{17}{12}$."
},
{
"role": "assistant",
"content": "$6188$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{7721}{7720}$."
},
{
"role": "assistant",
"content": "$7721$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{5}{4}$."
},
{
"role": "assistant",
"content": "$5$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{2333}{2333}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{7024}{7024}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{8067}{8066}$."
},
{
"role": "assistant",
"content": "$8067$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{6595}{6594}$."
},
{
"role": "assistant",
"content": "$6595$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{2086}{2084}$."
},
{
"role": "assistant",
"content": "$2174655$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{9978}{9977}$."
},
{
"role": "assistant",
"content": "$9978$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{4252}{4252}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{9194}{9194}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{10186}{10185}$."
},
{
"role": "assistant",
"content": "$10186$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{9116}{9116}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{54}{50}$."
},
{
"role": "assistant",
"content": "$316251$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{8}{4}$."
},
{
"role": "assistant",
"content": "$70$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{6533}{6532}$."
},
{
"role": "assistant",
"content": "$6533$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{2316}{2314}$."
},
{
"role": "assistant",
"content": "$2680770$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{7889}{7888}$."
},
{
"role": "assistant",
"content": "$7889$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{4262}{4260}$."
},
{
"role": "assistant",
"content": "$9080191$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{7189}{7189}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{3474}{3474}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{1710}{1710}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{6740}{6739}$."
},
{
"role": "assistant",
"content": "$6740$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{8112}{8111}$."
},
{
"role": "assistant",
"content": "$8112$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{8}{6}$."
},
{
"role": "assistant",
"content": "$28$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{534}{533}$."
},
{
"role": "assistant",
"content": "$534$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{6008}{6008}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{7501}{7500}$."
},
{
"role": "assistant",
"content": "$7501$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{1154}{1152}$."
},
{
"role": "assistant",
"content": "$665281$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{5953}{5953}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{3540}{3538}$."
},
{
"role": "assistant",
"content": "$6264030$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{9768}{9768}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{5452}{5452}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{211}{208}$."
},
{
"role": "assistant",
"content": "$1543465$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{\\frac{26685}{4}}{\\frac{26681}{4}}$."
},
{
"role": "assistant",
"content": "$\\frac{26685}{4}$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{3885}{3884}$."
},
{
"role": "assistant",
"content": "$3885$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{832}{832}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{4907}{4906}$."
},
{
"role": "assistant",
"content": "$4907$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{380}{380}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{2979}{2977}$."
},
{
"role": "assistant",
"content": "$4435731$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{2201}{2199}$."
},
{
"role": "assistant",
"content": "$2421100$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{1291}{1289}$."
},
{
"role": "assistant",
"content": "$832695$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{7681}{7681}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{4410}{4408}$."
},
{
"role": "assistant",
"content": "$9721845$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{5825}{5825}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{9758}{9757}$."
},
{
"role": "assistant",
"content": "$9758$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{8263}{8262}$."
},
{
"role": "assistant",
"content": "$8263$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{301}{298}$."
},
{
"role": "assistant",
"content": "$4499950$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{4323}{4321}$."
},
{
"role": "assistant",
"content": "$9342003$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{942}{941}$."
},
{
"role": "assistant",
"content": "$942$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{\\frac{7251}{2}}{\\frac{7247}{2}}$."
},
{
"role": "assistant",
"content": "$\\frac{52562499}{8}$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{\\frac{6669}{2}}{\\frac{6667}{2}}$."
},
{
"role": "assistant",
"content": "$\\frac{6669}{2}$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{7296}{7295}$."
},
{
"role": "assistant",
"content": "$7296$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{23}{10}$."
},
{
"role": "assistant",
"content": "$1144066$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{6108}{6107}$."
},
{
"role": "assistant",
"content": "$6108$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{23}{21}$."
},
{
"role": "assistant",
"content": "$253$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{149}{148}$."
},
{
"role": "assistant",
"content": "$149$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{1456}{1456}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{31}{28}$."
},
{
"role": "assistant",
"content": "$4495$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{7039}{7039}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{9781}{9781}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{73}{73}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{4870}{4869}$."
},
{
"role": "assistant",
"content": "$4870$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{2905}{2905}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{4508}{4507}$."
},
{
"role": "assistant",
"content": "$4508$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{\\frac{6477}{4}}{\\frac{6473}{4}}$."
},
{
"role": "assistant",
"content": "$\\frac{6477}{4}$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{3445}{3444}$."
},
{
"role": "assistant",
"content": "$3445$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{76}{72}$."
},
{
"role": "assistant",
"content": "$1282975$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{5164}{5163}$."
},
{
"role": "assistant",
"content": "$5164$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{398}{397}$."
},
{
"role": "assistant",
"content": "$398$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{938}{936}$."
},
{
"role": "assistant",
"content": "$439453$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{1577}{1575}$."
},
{
"role": "assistant",
"content": "$1242676$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{729}{727}$."
},
{
"role": "assistant",
"content": "$265356$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{9274}{9273}$."
},
{
"role": "assistant",
"content": "$9274$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{8559}{8558}$."
},
{
"role": "assistant",
"content": "$8559$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{5925}{5924}$."
},
{
"role": "assistant",
"content": "$5925$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{5031}{5031}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{4937}{4936}$."
},
{
"role": "assistant",
"content": "$4937$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{97}{96}$."
},
{
"role": "assistant",
"content": "$97$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{7154}{7154}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{464}{464}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{10106}{10105}$."
},
{
"role": "assistant",
"content": "$10106$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{4847}{4847}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{5622}{5621}$."
},
{
"role": "assistant",
"content": "$5622$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{8675}{8674}$."
},
{
"role": "assistant",
"content": "$8675$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{8114}{8113}$."
},
{
"role": "assistant",
"content": "$8114$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{229}{226}$."
},
{
"role": "assistant",
"content": "$1975354$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{8247}{8246}$."
},
{
"role": "assistant",
"content": "$8247$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{1741}{1740}$."
},
{
"role": "assistant",
"content": "$1741$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{7798}{7798}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{3011}{3009}$."
},
{
"role": "assistant",
"content": "$4531555$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{20}{15}$."
},
{
"role": "assistant",
"content": "$15504$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{2660}{2658}$."
},
{
"role": "assistant",
"content": "$3536470$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{8160}{8159}$."
},
{
"role": "assistant",
"content": "$8160$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{9518}{9518}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{\\frac{10539}{4}}{\\frac{10539}{4}}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{8591}{8590}$."
},
{
"role": "assistant",
"content": "$8591$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{5989}{5989}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Compute $\\binom{\\frac{31629}{4}}{\\frac{31629}{4}}$."
},
{
"role": "assistant",
"content": "$1$"
}
] | counting_and_statistics | binomial_coefficients |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.