Question 231490: How many different 5-card poker hands would contain only cards of a single suit?
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.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! How many different 5-card poker hands would contain only cards of a single suit?
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.
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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
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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.
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To be more formal, it's
13!/(5!*(13-5)!)
! is factorial. 5! = 5*4*3*2*1, etc.
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