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:
That fraction was reduced by dividing top and bottom by 460.
As a decimal that's 0.000133318192..., a very low probability.
Edwin
