Chapter 8.5, Problem 63E

To determine

To find: the number of different committees are possible from the 100 U.S senators.

Answer to Problem 63E

The number of ways to select senators are $2.53\times {10}^{17}$ .

Explanation of Solution

Given information:

As of May 2014, the U.S. senate committee of Indian Affairs had 14 members. Party affiliation is not a factor in selection.

Calculation:

Fifteen out of hundrad senators mean

  $\begin{array}{c}{}_{100}{C}_{15}=\frac{100!}{\left(100-15\right)!15!}\\ =\frac{100!}{85!15!}\\ =2.53\times {10}^{17}\end{array}$

Hence, the number of ways to select senators are $2.53\times {10}^{17}$ .