There are 2,598,960 5-card hands.
This is combinatorials, which is used in probability but is not probability itself.
The number of possible 4-card hands out of a 52 card deck is 270,725.
eleventeen
If the cards are all different then there are 13C7 = 1716 different hands.
If only one card is selected the probability is 12/13.If only one card is selected the probability is 12/13.If only one card is selected the probability is 12/13.If only one card is selected the probability is 12/13.
There are 1584 hands possible with 2 Kings, 2 Jacks and 1 other card which is not a King or a Jack.
The number of possible 4-card hands out of a 52 card deck is 270,725.
There are 1287 possible 5 card poker hands that contain only diamonds, i.e. a diamond flush.This is 13! / (13-5)! / 5!Since there are 2598960 possible 5 card poker hands, 52! / (52-5)! / 5!, the probability of drawing a diamond flush is 1287 in 2598960, or about 0.0004952.
eleventeen
There are 1716 of them.
are they dependent or independent? define success and failure for the 2 events. probability of success (EX: drawing a face card) = number of possible successes / total possible events. Multiply the two separate probabilities to get the probability that both occur.
Twelve: the fifth card can be anything but a queen.
There are 2597673 such hands.There are 2597673 such hands.
First, we determine the total number of five card hands possible. Since there are 52 cards, we simply pick the first card 52 ways, then the second card 51 ways, then the third card 50 ways, then the fourth card 49 ways, and finally the fifth card 48 ways. This gives a total of 52*51*50*49*48. Since the order that we pick the cards is unimportant, we divide this total by the number of ways of permuting five objects, which is 5! = 120. So, the total becomes 52*51*50*49*48/120 = 2598960. Note this is just (52 choose 5). Now that we know the number of possible hands, we simply divide the number of royal flushes (4) by the above 2598960: 4/2598960 = 0.000001539, the probability of getting a royal flush in the first 5 cards off the deck. Of course, depending on the type of poker being played, the probability will differ from this value. Omaha has a higher probability than Texas Hold'em, which has a higher probability than calculated above. Wild cards can drastically change the probability. If every card in the deck is wild, then the probability is 1 (if 5 of a kind isn't allowed) or 0 (if 5 of a kind is allowed).
If the cards are all different then there are 13C7 = 1716 different hands.
If only one card is selected the probability is 12/13.If only one card is selected the probability is 12/13.If only one card is selected the probability is 12/13.If only one card is selected the probability is 12/13.
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.
The probability of drawing a red card is 1/2 (26/52).The probability of drawing a face card is 3/13 (12/52).The probability of drawing a red face card is 3/26 (6/52).The probability of drawing a red card or a face card is 8/13 (32/52).2 out of 52or 1 out of 26.