Answer :
Answer:
The number of ways to select 5 diamonds and 3 clubs is 368,082.
Step-by-step explanation:
In a standard deck of 52 cards there are 4 suits each consisting of 13 cards.
Compute the probability of selecting 5 diamonds and 3 clubs as follows:
The number of ways of selecting 0 cards from 13 hearts is:
[tex]{13\choose 0}=\frac{13!}{0!\times(13-0)!} =\frac{13!}{13!}=1[/tex]
The number of ways of selecting 3 cards from 13 clubs is:
[tex]{13\choose 3}=\frac{13!}{3!\times(13-3)!} =\frac{13!}{13!\times10!}=286[/tex]
The number of ways of selecting 5 cards from 13 diamonds is:
[tex]{13\choose 5}=\frac{13!}{5!\times(13-5)!} =\frac{13!}{13!\times8!}=1287[/tex]
The number of ways of selecting 0 cards from 13 spades is:
[tex]{13\choose 0}=\frac{13!}{0!\times(13-0)!} =\frac{13!}{13!}=1[/tex]
Compute the number of ways to select 5 diamonds and 3 clubs as:
[tex]{13\choose0}\times{13\choose3}\times{13\choose5}\times{13\choose0} = 1\times286\times1287\times1=368082[/tex]
Thus, the number of ways to select 5 diamonds and 3 clubs is 368,082.