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A state runs a lottery called “Pick 6.” A player buys a lottery ticket showing 6 of the numbers from 1 through 40. Then a set of 6 numbers is chosen as the winning numbers, and anyone whose ticket matches those numbers wins a prize. (The order of the numbers does not matter.)

I know the answer is 1 over 40C6. Could you briefly explain how to get this solution?

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There are $N={40\choose 6}$ different combinations of numbers possible in the lottery, and the player chooses one of them. The probability of choosing the correct one is $1/N$.

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