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.

Guest Apr 5, 2021

#1**+1 **

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 $n=3$.

thedudemanguyperson Apr 5, 2021