Question

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

Answer 1

Exactly 4 blowers $\Rightarrow {5C}_4$
Remaining 7 players $\Rightarrow {12C}_7$
Answer $\Rightarrow {5C}_4]times12C^7$
$5\times \frac{12!}{7!5!}$
$\frac{\Rightarrow 5\times 8\times 9\times 10\times 11\times \times 12}{120}$
$\Rightarrow 3960$