52*51*50
------------- = 22100 three-card hands
3!
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You can draw C(52,13) = 52! /13! 39! = 635 013559 600 different 13-card hands from a deck of 52 cards.
There are 1716 of them.
The number of 5-card hands consisting of three of a kind can be calculated by choosing the rank for the three cards (13 options) and any two other cards (44 options remaining). Therefore, the number of 5-card hands consisting of three of a kind is 13 * 44 = 572.
Just one. After that you no longer have a card deck.
4*48*47/2 = 4512