Question

From among $30$ teachers in a school, one principal and one vice principal are to be appointed. In how many ways can this be done?

• A. $780$
• B. $8700$
• C. $870$
• D. $660$

Answer 1

The correct option is C $870$

We know that the number of permutation of "n" different things taken "k" at a time, with or without repetition is ${}_k^{n}P=\frac{n!}{(n-k)!}$

According to question we have to find permutation of $30$ teachers taking $2$ for the post of principal and vice principal.

So, number of permutations will be ${}_2^{30}P=\frac{30!}{(30-2)!}$

$\Rightarrow {}_2^{30}P=\frac{30!}{28!}=\frac{30\times 29\times 28!}{28!}$

$\Rightarrow {}_2^{30}P=30\times 29=870.$