# How many poker hands contain exactly two suits?

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Date created: Tue, Mar 2, 2021 12:00 PM
Date updated: Thu, Jun 23, 2022 2:48 PM

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Video answer: Permutations and combinations - 5 card poker hands

## Top best answers to the question «How many poker hands contain exactly two suits»

ie choose two suits, then from those 26 cards choose 5. Now subtract the two flush hands. ie get the number of hands with at most two suits then subtract the number of flush hands. (4 C 1)(13 C 5) is the number of flush hands in poker.

Video answer: How many 5 card poker games will have 2 pairs find probability

For the first rank we choose 2 suits out of 4, which can be done in $\binom{4}{2}$ ways. For the second rank we choose 2 suits out of 4, which can be done in $\binom{4}{2}$ ways. For the third rank we choose 1 suit out of 4, which can be done in $4$ ways. So the total number of hands is $\binom{13}{3}\cdot \binom{4}{2}\cdot \binom{4}{2}\cdot 4=41,184$ This is just a third of the correct number of hands.

Any hand having exactly two suits must have more of one suit that the other. It has 3 of this suit, and 2 of the other; or it has 4 of this suit and 1 of the other. There are 4 ways to pick the suit which appears most often in the hand.

Question: A) How Many Poker Hands Contain Exactly Two Hearts? B) How Many Poker Hands Contain At Least One Card In Each Suit?

Now 6 of the ways of getting the 2 pairs have the same suits represented for the 2 pairs, 24 of them have exactly 1 suit in common between the 2 pairs, and 6 of them have no suit in common between the 2 pairs.

Such a hand has exactly two cards of the same suit. To make such a hand: You can choose such a suit in 4 ways. You can choose the two cards from that suit in 13 choose 2 ways.

Thus of all the 5-card hands with all cards in a given suit, there are 1,287-10 = 1,277 hands that are not straight flush. Thus the total number of flush hands is 4 x 1277 = 5,108. Straight

In many forms of poker, one is dealt 5 cards from astandard deck of 52 cards. The number of different 5 -card pokerhands is. 52C5= 2,598,960. A wonderful exercise involves having students verify probabilitiesthat appear in books relating to gambling.

I know there are 52 cards in a deck and there are 4 different suits with 13 cards in each suit. From here, I am lost.-----It's 5 cards out of 13. The 1st is 1 of 13, then 1 of 12, etc = 13*12*11*10*9 = 154,440-----But, since 2, 3, 4, 5, 6 is the same as 6,5,4,3,2 it's necessary to divide by 5*4*3*2*1 = 120--> 154440/120 = 1287 possibilities.-----

cards. The 52 cards are categorized by 13 ranks from Two through Ace (Aces can be counted as both higher than King and lower than Two when needed, but can only count as one at a time in a hand), and by four suits: diamonds, hearts, spades, and clubs. In the game of poker, players attempt to assemble the best five-card hand according to the

Math 221 Counting Worksheet: Poker Hands A standard 52-card deck consists of 13 cards from each of 4 suits (spades, hearts, diamonds, clubs). The 13 cards have value 2 through 10, jack (J), queen (Q), king (K), or ace (A). Each value is a “kind” of card. The jack, queen, and king are called “face cards”. How many 5-card poker hands are there? 52