26 Black cards, choose 5

26 Choose 5 = 26C5 = 

The denominator will cancel entirely into the numerator, and
when you multiply what's left you get 65780 possible all-black hands.

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To get the denominator of the probability, we calculate the number of all
possible hands, whether they are all black, all red or mixed.

52 cards, choose 5

52 Choose 5 = 52C5 = 

The denominator will cancel entirely into the numerator, and
when you multiply what's left you get 2598960 possible hands.

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So the probability is 65780 out of 2598960, which is the fraction



That can be reduced by dividing top and bottom by 260, getting



or as a decimal, approximately 0.025310124 or about 0.025,

That's close to 1 out of 40.

that means that you'll average getting an all-black hand about
1 time out of 40.

Edwin