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jmc

counting and probability senior

Problem

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?
Solution
The number of ways to roll exactly 2 6's is , since there are 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 1 6 is , and the number of ways to roll no 6's is . So the probability is
Final answer
\frac{625}{648}