Question 958481
To get the numerator of the probability, we calculate the number of all black
hands, which is:
<pre>
26 Black cards, choose 5

26 Choose 5 = 26C5 = {{{matrix(1,9,"26*25*24*23*22"," ","<-five",factors, on,top,starting,with,26)/
matrix(1,16,"","","","","","","5*4*3*2*1"," ","<-five",factors, on,the,bottom,starting,with,5))}}}

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 = {{{matrix(1,9,"52*51*50*49*48"," ","<-five",factors, on,top,starting,with,52)/
matrix(1,16,"","","","","","","5*4*3*2*1"," ","<-five",factors, on,the,bottom,starting,with,5))}}}

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

{{{65780/2598960}}}

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

{{{253/9996}}}

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</pre>