Question

As of January 2005, the U.S. Senate Committee on Indian Affairs had 14 members. Assuming party affiliation was not a factor in selection, how many different committees were possible from the 100 U.S. senators?

Answer 1

Answer:  $4.42\times10^{16}$

Step-by-step explanation:

Given : The total number of U.S. senators = 100

The number of members in U.S. Senate Committee  = 14

Since Assuming party affiliation was not a factor in selection , we use combinations.

Formula : $^nC_r=\dfrac{n!}{r!(n-r)!}$

Then , the number of different committees were possible from the 100 U.S. senators :

$^{100}C_{14}=\dfrac{100!}{14!(100-14)!}\\\\=\dfrac{100\times99\times.....87\times86!}{14!86!}\\\\=\dfrac{100\times99\times.....87}{14\times13\times12.....\times1}\\\\\approx4.42\times10^{16}$

Hence, the number of different committees were possible from the 100 U.S. senators is $4.42\times10^{16}$ .