#Chapter 3. Combinatorics 3.2 Question 8 A die is rolled 30 times. What is the probability that a 6 turns up exactly 5 times?

Since the dice is rolled 30 times we can use (1/6)^(30)

P_5Sixs <- choose(30,5)/6^30
P_5Sixs
## [1] 6.446079e-19

What is the most probable number of times that a 6 will turn up? Since we get a 6 if we use (1/6)*30

(1/6) * 30
## [1] 5