# Question: Many states have a lottery game usually called a Pick 4

Many states have a lottery game, usually called a Pick-4, in which you pick a four-digit number such as 7359. During the lottery drawing, there are four bins, each containing balls numbered 0 through 9. One ball is drawn from each bin to form the four-digit winning number.

a. You purchase one ticket with one four-digit number. What is the probability that you will win this lottery game?

b. There are many variations of this game. The primary variation allows you to win if the four digits in your number are selected in any order as long as they are the same four digits as obtained by the lottery agency. For example, if you pick four digits making the number 1265, then you will win if 1265, 2615, 5216, 6521, and so forth, are drawn. The variations of the lottery game depend on how many unique digits are in your number. Consider the following four different versions of this game.

i. All four digits are unique (e.g., 1234)

ii. Exactly one of the digits appears twice (e.g., 1223 or 9095)

iii. Two digits each appear twice (e.g., 2121 or 5588)

iv. One digit appears three times (e.g., 3335 or 2722)

Find the probability that you will win this lottery in each of these four situations

a. You purchase one ticket with one four-digit number. What is the probability that you will win this lottery game?

b. There are many variations of this game. The primary variation allows you to win if the four digits in your number are selected in any order as long as they are the same four digits as obtained by the lottery agency. For example, if you pick four digits making the number 1265, then you will win if 1265, 2615, 5216, 6521, and so forth, are drawn. The variations of the lottery game depend on how many unique digits are in your number. Consider the following four different versions of this game.

i. All four digits are unique (e.g., 1234)

ii. Exactly one of the digits appears twice (e.g., 1223 or 9095)

iii. Two digits each appear twice (e.g., 2121 or 5588)

iv. One digit appears three times (e.g., 3335 or 2722)

Find the probability that you will win this lottery in each of these four situations

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