Question

A committee of 6 students is to be selected from 15 students in a fraternity.a. In how many ways can this be done?b. In how many ways can the group that will not take part be chosen?BB.a. The number of ways to form a 6-student committee is

Answer 1

A committee of 6 students is to be selected from 15 students in a fraternity.

a. In how many ways can this be done?

b. In how many ways can the group that will not take part be chosen?

Part a

Find out the combination 15C6

$15C6=\frac{n!}{r!(n-r)!}$

where

n=15

r=6

substitute

$\begin{gathered} 15C6=\frac{15!}{6!(15-6)!} \\ 15C6=\frac{15!}{6!(9!)!} \end{gathered}$

15C6=5,005

The answer part a is 5,005 ways

Part b

Find out 15C9

because

not take part to be chosen=15-6=9

n=15

r=9

substitute

$\begin{gathered} 15C9=\frac{15!}{9!(15-9)!} \\ 15C9=\frac{15!}{9!(6)!} \end{gathered}$

15C9=5,005 ways