Answer:
[tex] 12C5 *(12C3) = 792*220 =174240 ways[/tex]
Step-by-step explanation:
For this case we know that we have 12 cards of each denomination (hearts, diamonds, clubs and spades) because 12*4= 52
First let's find the number of ways in order to select 5 diamonds. We can use the combinatory formula since the order for this case no matter. The general formula for combinatory is given by:
[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]
So then 12 C5 would be equal to:
[tex] 12C5 = \frac{12!}{5! (12-5)!}=\frac{12!}{5! 7!} = \frac{12*11*10*9*8*7!}{5! 7!}= \frac{12*11*10*9*8}{5*4*3*2*1}=792[/tex]
So we have 792 was in order to select 5 diamonds from the total of 12
Now in order to select 3 clubs from the total of 12 we have the following number of ways:
[tex] 12C3 = \frac{12!}{3! 9!}=\frac{12*11*10*9!}{3! 9!} =\frac{12*11*10}{3*2*1}=220[/tex]
So then the numbers of ways in order to select 5 diamonds and 3 clubs are:
[tex] (12C5)*(12C3) = 792*220 =174240 ways[/tex]
