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

There are 5 bowlers and 12 other players in a team of 17 players we have to select 4 bowels out of 5 bowlers and 7 other players out of 12 other players.

$\therefore$ Number of ways of selection

= ${}^5{C}_4{\times }^{12}{C}_7$

= $\frac{5!}{4!1!}\times \frac{12!}{7!5!}$

= $\frac{5\times 4!}{4!}\times \frac{12\times 11\times 10\times 9\times 8\times 7!}{7!\times 5\times 4\times 3\times 2\times 1}$

= $5\times 792=3960.$