Question

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

Answer 1

There are total 5 bowlers and 12 batsman are available

Number of ways to select a team of 11 that includes exactly 4 bowlers.

= (7 batsman out of 12 batsman) and (4 bowlers out of 5 bowlers)

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

$=\frac{12\times 11\times 10\times 9\times 8}{5\times 4\times 3\times 2\times 1}\times 5=3960$

Required number of ways = 3960