Q: How many 3 card hands are possible from a standard deck of 52 cards?

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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.

26 of the 52 cards are black. For each of those cards, the second card in your hand may not be the same card, but it may be any of the 25 remaining ones. The third card, likewise, can not be the first two, but can be any of the 24 remaining. For a four card hand that's 26 * 25 * 24 * 23 = 358800 possible hands However, that number includes sets that are effectively duplicates (1,2,3,4 and 4,3,2,1 are both accounted for in that number, but for our purposes those are the same hand). We can arrange each set of cards 4 * 3 * 2 * 1 = 24 ways. So to remove those possibilities we take 358800/24 = 14950 possible hands of all black cards.

You can draw C(52,13) = 52! /13! 39! = 635 013559 600 different 13-card hands from a deck of 52 cards.

There are 2,598,960 possible five-card hands. There are 4 combinations of royal flushes in 5 cards. Therefore, the odds are 649,739:1. There are 20,358,520 possible six-card hands. There are 188 combos of royal flushes in 6 cards. Therefore, the odds are 108,290:1.

The maximum number of 5-card hands with 3 spades and 2 hearts is 4. The least is 0. There are 13 spade cards and if at least 3 spades are needed in a hand, only 4 hands can be formed.

Related questions

If the cards are all different then there are 13C7 = 1716 different hands.

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.

There are 15,820,024,220 ways.

Assuming the 52 cards are all different, the first card can be any of the 52, the second card can be any of the remaining 51, and the third card can be any of the remaining 50, so there are 52x51x50 different three card hands possible.

26 of the 52 cards are black. For each of those cards, the second card in your hand may not be the same card, but it may be any of the 25 remaining ones. The third card, likewise, can not be the first two, but can be any of the 24 remaining. For a four card hand that's 26 * 25 * 24 * 23 = 358800 possible hands However, that number includes sets that are effectively duplicates (1,2,3,4 and 4,3,2,1 are both accounted for in that number, but for our purposes those are the same hand). We can arrange each set of cards 4 * 3 * 2 * 1 = 24 ways. So to remove those possibilities we take 358800/24 = 14950 possible hands of all black cards.

The number of possible 4-card hands out of a 52 card deck is 270,725.

You can draw C(52,13) = 52! /13! 39! = 635 013559 600 different 13-card hands from a deck of 52 cards.

There are 2,598,960 possible five-card hands. There are 4 combinations of royal flushes in 5 cards. Therefore, the odds are 649,739:1. There are 20,358,520 possible six-card hands. There are 188 combos of royal flushes in 6 cards. Therefore, the odds are 108,290:1.

You can make 2,598,960 different 5 card hands (not counting permutations) with a standard 52 card deck.

The maximum number of 5-card hands with 3 spades and 2 hearts is 4. The least is 0. There are 13 spade cards and if at least 3 spades are needed in a hand, only 4 hands can be formed.

The highest number card in a standard deck of cards is the number ten. Some games use the picture cards to represent values higher than ten but there are no numbers on these cards.

There are 26 red cards and 26 black cards. 3 red cards can be chosen in 26C3 ways 2 black cards can be chosen in 26C2 ways The required answer is 26C3 X 26C2 ways. Answer: 1067742 S Suneja