We roll a fair 6-sided die 5 times. What is the probability that we get a 6 in at most 2 of the rolls?

The number of ways to roll exactly two 6's is \(\binom{5}{2}5^3\), since there are \(\binom{5}{2}\) choices for which of the two dice are 6, and there are 5 choices for each of the other 3 dice. Similarly, the number of ways to roll exactly one 6 is \(\binom{5}{1}5^4\), and the number of ways to roll no 6's is \(\binom{5}{0}5^5\). So the probability is \(\frac{\binom{5}{2}5^3+\binom{5}{1}5^4+\binom{5}{0}5^5}{6^5} = \frac{625}{648}\)