Charlie draws 5 cards out of a deck of 52. If he gets at least three of

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Charlie draws 5 cards out of a deck of 52. If he gets at least three of one suit, he discards the cards not of that suit and then draws until he again has 5 cards. For example, if he gets 3 hearts, 1 club, and 1 spade, he throws the 2 non hearts away and draws 2 more. What is the probability that he will end up with 5 cards of the same suit?

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