Solution:

The number of ways to select three teachers from 36 members is equal to the number of ways to nominate one principal, vice-principal, and teacher in charge.

As a result, three posts will be filled.

There are ³⁶C₁ = 36 methods to choose a principal.

There are ³⁵C₁ = 35 methods to choose vice-principal (35, since one position is already given)

There are ³⁴C₁ different ways to choose the teacher in charge (34, since two positions are already given)

As a result, there are ³⁶C₁ × ³⁵C₁ × ³⁴C₁ = 36 × 35 × 34 = 42840 options to appoint three teachers.