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The Powerball lottery is played twice each week in 28 states, the Virgin Islands, and the District of Columbia. To play Powerball a participant must purchase a ticket and then select five numbers from the digits 1 through 55 and a Powerball number from the digits 1 through 42. To determine the winning numbers for each game, lottery officials draw five white balls out of a drum with 55 white balls, and then one red ball out of a drum with 42 red balls. To win the jackpot, a participant’s numbers must match the numbers on the five white balls and the number on the red Powerball. Compute the number of ways the first five numbers can be selected.

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carlosego

Answer:

There are 3478761 ways to select the first 5 numbers

Step-by-step explanation:

As understood from the statement of this problem we assume that it does not matter the order in which the first 5 white balls are selected.

In this case it is a combination.

So, what we want to know is how many ways you can choose 5 white balls out of 55.

Then we use the formula of combinations:

[tex]C(n, x) = \frac{n!}{x! (n-x)!}[/tex]

Where you have n elements and choose x from them.

Then we look for:

[tex]C(55, 5) = \frac{55!}{5!(55-5)!}\\\\C(55, 5) = \frac{55!}{5!(50)!}\\\\C(55, 5) = 3478761[/tex]