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2024 SSMO Accuracy Round Problems/Problem 3

Problem

Three distinct random integers $a$, $b$, and $c$ are selected so that $1 \le a, b, c \le 10$. Let the probability that $5|a!+b!+c!$ be $\frac{m}{n}$, where $\gcd(m,n)=1$. Find $m+n$.

Solution

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