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How many ways are there to select 3 cards one after the other from a deck of 52 cards if the cards are not returned to the deck after being selected?
GersonMolina
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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∙ 12y ago
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