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Statistics - Probability

A lottery involves drawing five white balls out of a drum with 55 balls and then drawing one red ball out of a drum with 42 red balls. You can buy a $1 ticket and select five white numbers from (1-55 inclusive and one red number (from 1 - 42 inclusive). you win the lottery if you pick all five of the correct white balls and the correct red ball. how much would you have to spend to cover all possible combinations? If the jackpot was $100 million, assuming you'd be the only winner would this be a good idea?

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Update:

C(55, 5) and C(42, 1) are done on a calculator. Alternatively, you can use the formula C(n, r) = n! / {(n - r)! r!}

C(55, 5) = 55! / {(55 - 5)! 5!} = 55! / (50! 5!) = 3478761

C(42, 1) = 42 since ...

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