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*10^(16)`

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

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

`^(100)C_(14)=(100!)/(14!(100-14)!)\\\\=(100*99*.....87*86!)/(14!86!)\\\\=(100*99*.....87)/(14*13*12.....*1)\\\\\approx4.42*10^(16)`

Hence, the number of different committees were possible from the 100 U.S. senators is
`4.42*10^(16)` .