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The first card can be selected out of 52 cards, second from 51 cards, and the third from 50 cards. You may be tempted to give the answer as 52x51x50. But recognize that if you select

1 spade, 5 heart, 8 club, that is the same as

5 heart, 8 club, 5 heart

the order does not matter

So we need to find not nPr but nCr = 52C3 = (52!)/((49!)x(3!)) = (50 x 51 x 52)/6

which is 22100 ways

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