SOLUTION: MAT 145: Topics In Contemporary Math Permutations and Combinations 2. How many different 5-card poker hands are possible? Note: We are differentiating between the ace of clu

Question 1190904: MAT 145: Topics In Contemporary Math
Permutations and Combinations
2. How many different 5-card poker hands are possible? Note: We are differentiating between
the ace of clubs and the ace of spades: different suits means different hands!

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
52C5=2,598,960 different hands
choose 5 from 52.
That is 52!/5!*47!
That there are 52 ways to choose the first card, 51 the second, etc.
for the 5 cards you want,there are 5 ways to choose the first, and 120 ways to choose all 5, which is 5!
There are also 47 ways to choose the first card you don't want, and 47! ways to choose the 47
That is the denominator.
so it is 52*51*50*49*48*47!/47!*5*4*3*2*1

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