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How many poker hands can contain 3 Clubs and 2 Hearts?
(13x12x11x13x12)/ (5x4x3x2x1) = 1859
How many 5 card poker hands contain only red cards?
three
How many five card hands chosen from a standard deck contain two clubs and three hearts?
There are two smaller problems in this one. First, is the fraction formed by the probabilities of the cards desired, then also there's the permutations of this fraction. Multiplying them together gives the total probability. The permutations of the clubs and hearts in the hand are 4 + 3 + 2 + 1 = 10. Just for justification, there is (CCHHH), (CHCHH), (CHHCH), (CHHHC), (HCCHH), (HCHCH), (HCHHC), (HHCCH), (HHCHC), (HHHCC). So: P(two clubs, three hearts) = 10 * (13 * 12 * 13 * 12 * 11) / (52 * 51 * 50 * 49 * 48) = 10 * (2432111132) / (29325272131171) = (11 * 13) / (16 * 5 * 49 * 17) = 143/66,640
From a standard 52 card deck how many 5 card hands will have 3 spades and 2 hearts?
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.
How many 5 card poker hands consisting of three 8's and two cards that are not 8's are possible in a deck?
If the hand must contain three 8's and to cards that are not 8's - the total number of possibilities is 2801.
