Question

How many different committees can be formed from 12 teachers and 35 students if the committee consists of 4 teachers and 3 students?

Answer 1

Given that a committee of 4 teachers and 3 students is to be formed from 12 teachers and 35 students, we have

`12C4\text{ }*35C3`

Recall that:

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

This gives:

`\begin{gathered} (12!)/((12-4)!*4!)*(35!)/((35-3)!*3!) \\ =(12!)/(8!*4!)*(35!)/(32!*3!) \\ =(12*11*10*9*\cancel8!)/(\cancel8!*4*3*2*1)*(35*34*33*\cancel32!)/(\cancel32!*3*2*1) \\ =3239775 \end{gathered}`

Hence, the number of committees that can be formed is

`\begin{equation*} 3239775 \end{equation*}`