Posted in Poker September 28th, 2010
A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands?
are there consisting of four hearts and one spade?
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3 Comments on this post
Posted by juan dela cruz September 28th, 2010 at 4:27 pm
four hearts (13C4) and one spade (13C1):
= 13C4*13C1
= 13*12*11*10/(4*3*2*1)*13
= 9295 hands
Posted by bdwolfhound September 28th, 2010 at 4:50 pm
As each time a heart is dealt, the number remaining is one less, so 4 hearts can be dealt 13 x 12 x 11 x 10 = 17160 ways
For each set of 4 hearts, there can be 13 spades. The total number of hands is 13 x 17160 = 223080
Posted by Mark F September 28th, 2010 at 5:21 pm
Just an added note, in Texas Hold’em there are 1362 possible starting hands. The other answers are dead on by th way.