Chapter 2.1, Problem 24E

Rolling 4 Sixes If you roll N dice, then the probability $p=p\left(N\right)$ that you will get exactly 4 sixes is given by

$p=\frac{N\left(N-1\right)\left(N-2\right)\left(N-3\right)}{24}\times {\left(\frac{1}{6}\right)}^4{\left(\frac{5}{6}\right)}^{N-4}$

a. What is the probability, rounded to three decimal places, of getting exactly 4 sixes if 10 dice are rolled? How many times out of 1000 rolls would you expect this to happen?

b. How many dice should be rolled so that the probability of getting exactly 4 sixes is the greatest?