If you roll a fair 6 sided die 5 times, rolling a 4 is considered to be a success, what are the chances of rolling exactly 3 successes?

Answer 1

The probability of k successes out of n tries for a success of P and a failure (1-P) is

C_n^k (P)^k(1-P)^n-k)

where the first part is the combination of n things k at a time. Here n = 5, k = 3 and P is 1/6