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

2496144

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) =
`(n!)/(r!(n-r)!)`

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

C(24,13) =
`(24!)/(13!(24-13)!)`

=
`(24!)/(13!*11!)`

=
`(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

=
`(24*23*22*21*20*19*18*17*16*15*14)/(11!)`

=
`(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