The are 52 possible outcomes if you pick a card from a deck of 52.
52*51*50 ------------- = 22100 three-card hands 3!
This is a permutation, which is from 52 select 3, or52P3, or 132600. The other way to think of this is you have 52 choices for the first card, 51 choices for the second card, and 50 choices for the third card. Therefore you have 52*51*50 possible hands or 132600.
You can draw C(52,13) = 52! /13! 39! = 635 013559 600 different 13-card hands from a deck of 52 cards.
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.
eleventeen
There are 2,598,960 5-card hands. This is combinatorials, which is used in probability but is not probability itself.
If the cards are all different then there are 13C7 = 1716 different hands.
The are 52 possible outcomes if you pick a card from a deck of 52.
There are 1584 hands possible with 2 Kings, 2 Jacks and 1 other card which is not a King or a Jack.
52*51*50 ------------- = 22100 three-card hands 3!
This is a combinations question. There are (52 C 13) possible hands. This is 52!/((13!)((52-13)!)) = 635013559600
This is a permutation, which is from 52 select 3, or52P3, or 132600. The other way to think of this is you have 52 choices for the first card, 51 choices for the second card, and 50 choices for the third card. Therefore you have 52*51*50 possible hands or 132600.
(4 nCr 3)x(4 nCr 2)=4x6=24
You can draw C(52,13) = 52! /13! 39! = 635 013559 600 different 13-card hands from a deck of 52 cards.
23
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.