If the hand must contain three 8's and to cards that are not 8's - the total number of possibilities is 2801.
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.
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.
4*48*47/2 = 4512
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.
Poker hands consist of only five cards, three pair is impossible.
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.
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.