rom a committee of 8 persons, in how many ways can we choose a chairman

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 = ${ }^{8} \mathrm{P}_{2}=\frac{8 !}{(8-2) !}=\frac{8 !}{6 !}=\frac{8 \times 7 \times 6 !}{6 !}=8 \times 7=56$