Question

In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?

Answer 1

Out of 17 players, 5 players are bowlers.

A cricket team of 11 players is to be selected in such a way that there are exactly 4 bowlers.

4 bowlers can be selected in ⁵C₄ ways and the remaining 7 players can be selected out of the 12 players in ¹²C₇ ways.

Thus, by multiplication principle, required number of ways of selecting cricket team