Question

A committee must be formed with 4 teachers and 4 students. If there are 7 teachers to choose from, and 9 students, how many different ways could the committee be made?

Answer 1

4,410

Step-by-step explanation

The number of ways we can choose 4 teachers from 7 teachers is,

`_7C_4=(7!)/((7-4)!*4!)=(7*6*5*4!)/(3!*4!)=(7*6*5)/(3*2)=(7*6*5)/(6)=7*5=35`

There are 35 ways of choosing 4 teachers out of 7.

And the number of ways we can choose 4 students from 9 students is,

`\begin{gathered} _9C_4=(9!)/((9-4)!*4!)=(9*8*7*6*5*4!)/(5!*4!)=(9*8*7*6*5)/(5*4*3*2) \\ _9C_4=(9*8*7)/(4)=(9*(2*4)*7)/(4)=9*7*2=126 \end{gathered}`

There are 126 ways of choosing 4 students out of 9.

The committee is formed by 4 teachers and 4 students. The number of ways it can be made is,

`_7C_4*_9C_4=35*126=4,410`

Hence, there are 4,410 ways to choose 4 students and 4 teachers out of 9 students and 7 teachers.