Answer:
2496144
Step-by-step explanation:
Total number of members of the senate on the finance committee (n)= 24
Number of members in each subcommittee(r) = 13
We need to make use of the combinations formula
C(n,r) = [tex]\frac{n!}{r!(n-r)!}[/tex]
1) Plugging in the values of n and r into formula, we get
C(24,13) = [tex]\frac{24!}{13!(24-13)!}[/tex]
= [tex]\frac{24!}{13!*11!}[/tex]
= [tex]\frac{24*23*22*21*20*19*18*17*16*15*14*13!}{13!*11!}[/tex]
2) Cancelling out the 13! from the top and bottom, we get
= [tex]\frac{24*23*22*21*20*19*18*17*16*15*14}{11!}[/tex]
= [tex]\frac{24*23*22*21*20*19*18*17*16*15*14}{11*10*9*8*7*6*5*4*3*2*1}[/tex]
3) Upon simplifying the numbers on the top and bottom, we get
C(24,13) = 2496144
