Question

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

• A. $10$
• B. $15$
• C. $2100$
• D. $8$

Answer 1

The correct option is C $2100$

There are $C(5,2)$ ways to select $2$ teachers from $5$ and $C(10,4)$ ways to select $4$ students from $10$ where, $C(n,r)$ is the combinations of $n$ items taken $r$ at a time.

Using the multiplication counting principle, the number of different committees that can be formed is given by:

$C(5,2)\cdot C(10,4)=2100$.

Hence, $2100$ committees can be formed from $5$ teachers and $10$ students.