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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?
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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
\[= \frac{36!}{\left( 36 - 2 \right)!}\]
\[ = \frac{36!}{34!}\]
\[ = \frac{36 \times 35 \times 34!}{34!}\]
\[ = 36 \times 35 \]
\[ = 1260\]
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