To calculate the number of 5-card Poker hands consisting of three 4's and two cards that are not 4's, we first choose 3 out of the 4 available 4's, which can be done in (\binom{4}{3} = 4) ways. Next, we need to select 2 cards from the remaining 48 cards (since there are 52 cards total and 4 are 4's), which can be done in (\binom{48}{2} = 1,176) ways. Therefore, the total number of such hands is (4 \times 1,176 = 4,704).
If the hand must contain three 8's and to cards that are not 8's - the total number of possibilities is 2801.
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.
If the cards are all different then there are 13C7 = 1716 different hands.
2,560
23
A suit contains 13 cards of the same kind. 4 cards may be choosen out of 13 in 13C4 (715) ways. There are 4 suits. Therefore, the number of possible hands for getting 4 cards of the same suit is 4 x 13C4 = 4 x 715 = 2,860.
13 x 12 x 11 x 49 x 48 13 x 12 x 11 because there are 13 possible cards for any given suit, then 12 more of the same suit, then 11 more for the same suit. At this point, you have 49 cards left, then 48. So there are 4,036,032 possible hands like that.
4*48*47/2 = 4512
Poker hands consist of only five cards, three pair is impossible.
In a game of euchre using a 24-card deck, where each player is dealt 5 cards, the number of possible hands can be calculated using combinations. Specifically, the number of ways to choose 5 cards from a 24-card deck is given by the combination formula ( \binom{n}{k} ), which is ( \binom{24}{5} = \frac{24!}{5!(24-5)!} = 42,504 ). Thus, there are 42,504 possible euchre hands.
The ranking criteria for low poker hands are based on the lowest possible combination of cards, with the best hand being the one with the lowest value cards. The lowest hand in poker is called a "lowball" hand, and the ranking is determined by the value of the cards, with the lowest value cards being the best hand.
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.