37999500 committees can be formed from 11 teachers and 50 students.
Solution:
Using combination formula, [tex] \bold{n C_{r}=\frac{n !}{(n-r) ! r !}} [/tex]
‘n’ represents total number of items and ‘r’ indicates number of item being chosen.
[tex]\begin{array}{l}{\text { (3 out of } 11 \text { teachers } \times 4 \text { out of } 50 \text { students })} \\ \\{(\mathrm{n}=11, \mathrm{r}=3) \times(\mathrm{n}=50, \mathrm{r}=4)} \\\\ {11 C_{3} \times 50 C_{4}=\left(\frac{11 !}{3 !(11-3) !}\right) \times\left(\frac{50 !}{4 !(50-4) !}\right)} \\\\ {=\left(\frac{11 !}{3 ! 8 !}\right) \times\left(\frac{50 !}{4 ! 46 !}\right)=165 \times 230300=37999500}\end{array}[/tex]
