Question 1050194
<pre><b>
Choose the 8 spades from the 13 spades in 13C5 ways
For each of those, choose the remaining 
 5 from the 26 hearts and clubs in 26C5 ways.

So there are (13C8)(26C5) "successful" hands.

That's the numerator of the desired probability.

The denominator is the number of 13-card hands from
the entire deck of 52.  That's 52C13

Answer:  {{{((13C8)(26C5))/(52C13)}}}{{{""=""}}}{{{1287*65780/635013559600}}}{{{""=""}}}{{{84658860/635013559600}}}{{{""=""}}}{{{184041/1380464260}}}

That fraction was reduced by dividing top and bottom by 460.

As a decimal that's 0.000133318192..., a very low probability.

Edwin</pre><b>