Texas Holdem Poker Hands

How many five card poker hands have four of a kind and one other card?

1. Rodney F, on August 26th, 2010 at 4:15 am Said:

   there are 13 suits so it would be 13
   References :

2. Jules, on August 26th, 2010 at 4:23 am Said:

   624

   There are 13 cards per suit, and you cannot have the other card be the same number. Therefore your possible combinations are 13 x 12, or 156. However, since there are four different suits, the single card could be a heart, diamond, spade, or club. Because of that, you have to multiply the answer by 4.

   13 x 12 x 4 = 624
   References :
   http://binomial.csuhayward.edu/poker.html

3. Rob L, on August 26th, 2010 at 4:46 am Said:

   Number of distinct five card hands:

   52!/((52-5)!(5!))=2,598,960

   Number of four of a kinds = 13 (one of each suit)

   Number of ways to pick the fifth card = 52-4=48

   So you have 48*13=624 ways, and if you would like the probability:

   2.400960384*10^-4

   d)
   References :

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