Many states in the U.S.A 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. 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. Find the probability that you will win this lottery in each of these four situations Two digits each appear twice (e.g., 2121 or 5588)

Question

 Many states in the U.S.A 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.

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

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

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