Question

From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?

Answer 1

From a committee of 8 persons, a chairman and a vice chairman are to be chosen in such a way that one person cannot hold more than one position.

Here, the number of ways of choosing a chairman and a vice chairman is the permutation of 8 different objects taken 2 at a time.

Thus, required number of ways =$^8P_2=\frac{8!}{(8-2)!}=\frac{8!}{6!}$
$=\frac{8\times7\times6!}{6!}=8\times7=56$