From among the 36 teachers in a school, one principal and one vice-principal are to be appointed.

Here, we need to permute 2 teachers out of the 36 available teachers.

It can also be understood as the arrangement of 36 teachers, taken two at a time.

∴ Required number of ways = 36P2

$=\frac{36 !}{(36-2) !}$

$=\frac{36 !}{34 !}$

$=\frac{36 \times 35 \times 34 !}{34 !}$

$=36 \times 35$

$=1260$