4(13c4)(39c1) = (4)(715)(39)=1,11,540
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.
Asssuming you mean in a 13 card hand, to get exactly nine cards in a suit, there are 4 x C(13,9) x C(39,4) possible hands out of C(52,13) total hands. That is 4 x 58,809,465 / 635,013,559,600 = 0.000370445412454, or about 1 in 2700.
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.
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.
4(13c4)(39c1) = (4)(715)(39)=1,11,540
2,560
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.
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.
If the cards are all different then there are 13C7 = 1716 different hands.
Asssuming you mean in a 13 card hand, to get exactly nine cards in a suit, there are 4 x C(13,9) x C(39,4) possible hands out of C(52,13) total hands. That is 4 x 58,809,465 / 635,013,559,600 = 0.000370445412454, or about 1 in 2700.
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.
23
Poker hands consist of only five cards, three pair is impossible.
All poker hands consist of five cards. In Texas Holdem, you can use two, one or none from your hand and three, four or five of the community cards (the "board"). Because all hands are five cards, it is not possible to have a four-card run, or straight. It counts for nothing.
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.
It is not possible to have 3 pair in a game of Texas hold'em because you can only use 5 cards out of 7 and 3 pair uses 6. A straight of 5 cards is a valid hand. The full list of Poker Hand Rankings contains 10 hands.