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?
Solution:
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
$=\frac{36 !}{(36-2) !}$
$=\frac{36 !}{34 !}$
$=\frac{36 \times 35 \times 34 !}{34 !}$
$=36 \times 35$
$=1260$
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