Question

From among the $36$ teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?

Answer 1

Calculate the number of ways to appoint a principal and vice-principal

Given, there are $36$ teachers.

Everyone has an equal chance of being selected as a principal.

So, the principal can be appointed in $36$ ways.

When $1$ person is appointed as principal, we are left with $35$ teachers.

Out of these $35$ teachers, we can select $1$ vice-principal.

So, a vice-principal can be selected in $36-1=35$ ways.

Hence, the number of ways in which a principal and vice-principal can be selected$=36\times 35=1260$

Therefore, we can select a principal and vice-principal from $36$ teachers in $1260$ ways.