Chapter 16.3, Problem 15P

You are making up a game for a fund-raiser. You take 5 table-tennis balls, number them from 1 to 5, and put all 5 in a brown bag. Contestants will pick the 5 balls out of the bag one at a time, without looking, and line the balls up in the order they were picked. If the contestant picks 1, 2, 3, 4, 5, in that order, then the contestant wins a prize of $2. Otherwise, the contestant wins nothing. Each contestant pays $1 to play.
a. What is the probability that a contestant will win the prize? Explain your reasoning.
b. If 240 people play your game, then approximately how many people would you expect to win the prize? Why?
c. Based on your answer to part (b), about how much money would you expect your game to earn (net) for the fund-raiser if 240 people play? Explain.