Question 975208
Probability of a 3 is (1/6)

This is a binomial with 15C5*(1/6)^5*(5/6)^10 = 0.0624

There are 15 rolls and 3003 different ways 5 threes can come up.
The overall probability is that time (1/6)^5 times and (5/6)^10 times.

The expected value would be 2.5, so this is reasonable.

While the numbers are too small to use the normal approximation, the variance is np(1-p)=75/36
The standard deviation would be about 1.35.

This is about 2 sd s above the mean, so again it is in the range of what one would expect.