Question

how many different committees can be formed from 11 teachers and 50 students if the committee consists of 3 teachers and 4 students?

Answer 1

37999500 committees can be formed from 11 teachers and 50 students.

Solution:

Using combination formula,
`\bold{n C_(r)=(n !)/((n-r) ! r !)}`

‘n’ represents total number of items and ‘r’ indicates number of item being chosen.

`\begin{array}{l}{\text { (3 out of } 11 \text { teachers } * 4 \text { out of } 50 \text { students })} \\ \\{(\mathrm{n}=11, \mathrm{r}=3) *(\mathrm{n}=50, \mathrm{r}=4)} \\\\ {11 C_(3) * 50 C_(4)=\left((11 !)/(3 !(11-3) !)\right) *\left((50 !)/(4 !(50-4) !)\right)} \\\\ {=\left((11 !)/(3 ! 8 !)\right) *\left((50 !)/(4 ! 46 !)\right)=165 * 230300=37999500}\end{array}`