Question

A school committee consists of $2$ teachers and $4$ students. Find the number of different committees that can be formed from $5$ teachers and $10$ students.

Answer 1

The number of combinations of $2$ out of $5$ teachers$=10$.

The number of combinations of $4$ students out of $10=210$.

Combining these we get $210\times 10=2100$ combinations of teachers and students in the committee.