[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {u: 3, j: 2, g: 3}, shuffle the letters in the word, what is the probability of no letter 'g' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}

dataset: MATH


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {i: 4, l: 6}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {r: 3, w: 1, p: 2, n: 2}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {w: 4, d: 2, e: 4}, shuffle the letters in the word, what is the probability of no letter 'e' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {g: 2, q: 3, o: 3}, shuffle the letters in the word, what is the probability of no letter 'g' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {e: 2, q: 2, i: 4}, shuffle the letters in the word, what is the probability of no letter 'e' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {y: 2, l: 3, n: 4, d: 1}, shuffle the letters in the word, what is the probability of no letter 'n' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {x: 3, n: 5}, shuffle the letters in the word, what is the probability of no letter 'n' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {x: 1, h: 3, f: 3, z: 3}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {o: 3, p: 1, t: 3, f: 2}, shuffle the letters in the word, what is the probability of no letter 't' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {m: 5, o: 1, h: 2, k: 1}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {u: 4, o: 2, l: 3}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {c: 1, o: 3, i: 3, z: 3}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {c: 3, o: 4, v: 3}, shuffle the letters in the word, what is the probability of no letter 'c' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {g: 5, s: 3}, shuffle the letters in the word, what is the probability of no letter 'g' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {i: 1, y: 3, l: 3, m: 3}, shuffle the letters in the word, what is the probability of no letter 'i' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {c: 4, z: 3, t: 3}, shuffle the letters in the word, what is the probability of no letter 'c' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {x: 2, m: 3, v: 2, p: 3}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {s: 4, g: 6}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {f: 2, b: 1, r: 3, y: 2}, shuffle the letters in the word, what is the probability of no letter 'b' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {s: 2, i: 4, g: 2}, shuffle the letters in the word, what is the probability of no letter 'g' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {a: 3, e: 6}, shuffle the letters in the word, what is the probability of no letter 'e' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {v: 2, d: 2, j: 2, p: 2}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {c: 3, g: 3, e: 2, t: 1}, shuffle the letters in the word, what is the probability of no letter 'c' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {y: 5, v: 2, h: 3}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {j: 3, h: 6}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {b: 4, f: 6}, shuffle the letters in the word, what is the probability of no letter 'f' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {g: 2, s: 2, b: 4}, shuffle the letters in the word, what is the probability of no letter 'b' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {k: 6, n: 4}, shuffle the letters in the word, what is the probability of no letter 'n' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {j: 3, h: 3, b: 2}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {h: 4, z: 2, w: 2}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {g: 2, e: 3, f: 3, y: 1}, shuffle the letters in the word, what is the probability of no letter 'e' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {l: 1, w: 4, m: 2, y: 1}, shuffle the letters in the word, what is the probability of no letter 'm' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {x: 5, p: 3}, shuffle the letters in the word, what is the probability of no letter 'p' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {y: 3, n: 5, h: 1, u: 1}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {u: 2, d: 7}, shuffle the letters in the word, what is the probability of no letter 'u' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {v: 6, i: 4}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {z: 2, y: 2, w: 1, e: 3}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {o: 2, q: 2, m: 4}, shuffle the letters in the word, what is the probability of no letter 'm' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {d: 5, m: 4}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {l: 3, t: 1, k: 2, e: 3}, shuffle the letters in the word, what is the probability of no letter 't' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {u: 1, r: 3, p: 4, b: 2}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {x: 2, s: 3, t: 2, e: 2}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {r: 3, d: 1, k: 1, w: 4}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {d: 2, s: 2, v: 3, h: 2}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {v: 2, t: 3, i: 4}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {n: 4, s: 2, v: 3}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {u: 1, l: 4, s: 1, h: 2}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {p: 4, g: 4}, shuffle the letters in the word, what is the probability of no letter 'g' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {c: 1, n: 3, j: 2, z: 3}, shuffle the letters in the word, what is the probability of no letter 'n' occupy any of their original positions?
If the probability can be written as the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.

Present the answer in LaTex format: \boxed{Your answer}