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# probability

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n fair 6-sided dice are simultaneously rolled. The probability that exactly two of them show a number other than 1 is 25/72. Find n.

Apr 5, 2021

You can just experiment. For $3$ dice, there are $\binom{3}{2}$ ways to arrange and $\frac{5}{6}\cdot \frac{5}{6}\cdot \frac{1}{6}$ probability. This yields $\frac{25\cdot 3}{216}=\frac{25}{72}$ which works. So $n=3$.