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In games of the KENO or LOTTO style, the bettor selects numbers from a fixed set

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 In games of the KENO or LOTTO style, the bettor selects numbers from a fixed set. Then the game operator selects another set of numbers, and the bettor wins according to the number of matches.   

a.​Suppose that the game uses the numbers 1 through 50, and suppose that the operator selects eight of these. If the bettor selects five numbers, find the probability that there are exactly five matches. HINT: Think Hypergeometric

b.​Suppose that the game uses the numbers 1 through 50, and suppose that the operator selects ten of these. If the bettor selects five numbers, find the probability that there are exactly five matches. Also note whether this probability is larger or smaller than the probability in a.   

c.​Suppose that the game uses the numbers 1 through 50, and suppose that the operator selects ten of these. If the bettor selects six numbers, find the probability that there are exactly six matches. Note whether the probability here is larger or smaller than the probability in b.

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[Solved] In games of the KENO or LOTTO style, the bettor selects numbers from a fixed set

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