If a pick three player (see Exercise 19) opts for “box play,” the player wins if his sel...

If a pick three player (see Exercise 19) opts for “box play,” the player wins if his selection matches the winning number in any order. For example, if he selected the number 157, he wins if the winning number is 715 or any other reordering of 157.

a. How many different winning box play numbers are there if the three digits are different? That is, how many different ways are there to reorder a number such as 157?

b. Find the probability of winning with box play if the three digits are different.

c. How many different winning box play numbers are there if two digits are the same? That is, how many different ways are there to reorder a number such as 266?

d. Find the probability of winning with box play if two digits are the same.

(Reference Exercise 19)

“Pick three” games are played in thirty-six states. In this game, the player selects a three-digit number, such as 157. Also, the state selects a three-digit winning number.

a. How many different three-digit numbers are there? Explain your reasoning.

b. If the player opts for “straight play,” she wins if her selecting matches the winning number in exact order. For example, if she selected the number 157, she wins only if the winning number is 157. How many different winning straight play numbers are there?

c. Find the probability of winning with straight play.