Question

There are 24 members of the senate on the finance committee, how many different 13 member subcommittees can be chosen to review the current energy legislation

Answer 1

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) = $\frac{n!}{r!(n-r)!}$

1) Plugging in the values of n and r into formula, we get

C(24,13) = $\frac{24!}{13!(24-13)!}$

= $\frac{24!}{13!*11!}$

= $\frac{24*23*22*21*20*19*18*17*16*15*14*13!}{13!*11!}$

2) Cancelling out the 13! from the top and bottom, we get

= $\frac{24*23*22*21*20*19*18*17*16*15*14}{11!}$

= $\frac{24*23*22*21*20*19*18*17*16*15*14}{11*10*9*8*7*6*5*4*3*2*1}$

3) Upon simplifying the numbers on the top and bottom, we get

C(24,13) = 2496144