Chapter 7.1, Problem 39E

a player buys a Mega Millions ticket in many states (see Exercise 38), the player can also buy the Megaplier, which multiplies the size of a prize otiier than a jackpot by a multiplier ranging from two to five, The Megaplier is drawn using a pool of 15 balls, with five marked 2X, six marked 3X, three marked $ and one marked 5X, where each ball has the same likelihood of being drawn, Find the probability that a player who buys a Mega Millions ticket and the Megaplier wins

1. $5,000,000? (Ihe only way to do this is to match the first five numbers drawn but not the sixth number drawn, with Megaplier 5X.)
2. $30,000? (The only way to do this is to match exactly four of the first five numbers drawn and the sixth number drawn, with Megaplier 3X.)
3. $20? (The three ways to do this are to match exactly three of the first five numbers drawn, but not the sixth number drawn, or exactly two of the first five numbers and thesixth number, with Megaplier 2X, or to match exactly one of the first fivenumbers and the sixth number, with Megaplier 5X.)
4. $8? (Ihe two ways to do this are to match exactly one of the first five numbers and the sixth number drawn, with a multiplier of 2X, or to match the sixth number but none of the first five numbers, with Megaplier 4X)