Consider the Coupon Collector’s Problem: 10 different coupons are distributed into cereal boxes, one per box, so that any randomly selected box is equally likely to have any of the 10 coupons inside. Write a program to simulate the process of buying cereal boxes until all 10 distinct coupons have been collected. For each run, keep track of how many cereal boxes you purchased to collect the complete set of coupons. Then use your program to answer the following questions.
a. What is the probability you collect all 10 coupons with just 10 cereal boxes?
b. Use counting techniques to determine the exact probability in (a).

c. What is the probability you require more than 20 boxes to collect all 10 coupons?

d. Using techniques from Chapters 3 and 5, it can be shown that it takes about 29.3 boxes, on the average, to collect all 10 coupons. What’s the probability of collecting all 10 coupons in fewer than average boxes (i.e., less than 29.3)?