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

where

n=15

r=6

substitute

`\begin{gathered} 15C6=(15!)/(6!(15-6)!) \\ 15C6=(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=(15!)/(9!(15-9)!) \\ 15C9=(15!)/(9!(6)!) \end{gathered}`

15C9=5,005 ways