Three fives dice toss If four dice are tossed, find the probability that exactly 3 fives will show ( answer to the nearest thousandth in the for 0.xxx)?

HINT: Imagine rolling the dice one at a time. Say that a set of four rolls is good if exactly $3$ of the $4$ are fives. Then there are $4$ kinds of good roll: the non-five can come on the first die, the second, the third, or the fourth. Suppose, for example, that it comes on the second roll; let’s calculate the probability of this outcome.


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*The first roll was a five; that occurs with probability $\frac16$. The second roll was not a five; that occurs with probability $1-\frac16$. The third roll was a five again: probability $\frac16$. And the fourth roll was also a five: again probability $\frac16$. How do you combine these numbers to get the probability of a good roll with the non-fine coming on the second die?

*What are the probabilities of the other three kinds of good sets of rolls?

*How do you combine these probabilities to get the total probability of a good set of rolls?
