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

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Solution

One principal and one vice-principal are to be appointed.
$∴$ Total number of ways = Number of arrangement of 36 things taken two at a time = $36_{p_{2}}$
= $\frac{36!}{(36 - 2)!}$
= $\frac{36!}{34!}$
= $\frac{36 \times 35 \times 34!}{34!}$
= $36 \times 35 = 1260$ Hence, Total number of ways to oppoint one principal and one vice-principal are 1260.

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

One principal and one vice-principal are to be appointed. ∴ Total number of ways = Number of arrangement of 36 things taken two at a time = 36p2 = 36!(36−2)! = 36!34! = 36×35×34!34! = 36×35=1260 Hence, Total number of ways to oppoint one principal and one vice-principal are 1260.