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?

Question

Philoid · Accepted Answer

Given that we need to select 11 players out of available 17 players in which 5 players are bowlers.

It is also mentioned that each team should contain exactly 4 bowlers.

Let us assume the no. of ways of selection be N.

⇒ N = (no. of ways of selecting 4 bowlers out of 5) × (no. of ways of selecting 7 players from remaining 12 players)

⇒ N = (⁵C₄) × (¹²C₇)

We know that ,

And also n! = (n)(n – 1)......2.1

⇒

⇒ N = 5 × 792

⇒ N = 3960