13 13
# of Poker hands with 3 clubs & 2 heards = ( ) ( )
3 2
= (13!)( 13!) / (10!*3!*11!*2)
= (13!)( 13!) / (10!*11!*12)
= (13!)( 13!) / (10!*12!)
= 13 * 13* 12 * 11
= 22308 #
(13x12x11x13x12)/ (5x4x3x2x1) = 1859
three
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
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.
If the hand must contain three 8's and to cards that are not 8's - the total number of possibilities is 2801.
(13x12x11x13x12)/ (5x4x3x2x1) = 1859
three
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
Poker pays no attention to the ranking of suits. Two royal flushes will split the pot, regardless of the suits. It is important in bridge, but not in poker. There is one application of suits in poker. When establishing the "first bet" person in stud (high card) or razz (low card) and the choice is between two identical cards then the suit breaks the tie. Use the same ranking as in bridge (spades,hearts,diamonds,clubs; high to low.) Example, in stud if the high card is a queen and there are two queens, a heart and a club, the heart is the high card and begins the betting. Also, in Texas Hold'em, during the initial deal when one face-up cards is dealt to all the players to establish who gets the dealer button first, if two equally ranked cards are dealt then, and only then, do the suits come into play. For example, if two players are dealt a Jack, one hearts and one clubs, then the heart would get it. The ranking of the suits is the same for all card games. Spades, hearts, diamonds, and clubs.
well T.P. with our hearts and hands
The probability is 0.0599
well T.P. with our hearts and hands
In Texas Hold'em each player has to use five cards out of seven to make a hand. You don't win rounds, the rounds are just for betting. You have to win the hand after all the community cards are revealed. You associate your cards with the community cards by seeing what you have and what is exposed. For example, if a player is holding a 10 of spades and a 4 of hearts and the flop reveals a 10 of hearts, 6 of diamonds, and a 2 of hearts, the player has a pair of tens. The player also has the potential to fill in a flush, all hearts, or a straight, 2,3,4,5,6. If the turn reveals a King of clubs, then the player has a pair of 10's with a King high, there is no longer a possibility of a flush or straight. A player can use any five cards to make the best possible hand, they don't have to use the cards in their hands, although using just the community cards does not usually win the hand.
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.
The story "Hearts and Hands" is told by an omniscient narrator.
The story "Hearts and Hands" is told by an omniscient narrator.
The clubs normally allow you to touch the girls if they put their hands on your hands and move them to their body.