A cricket team of 11 players is to be selected from 16 players including 5 bowlers and 2 wicketkeepers. In how many ways can a team be selected so as to consist of exactly 3 bowlers and 1 wicketkeeper?

Question

Philoid · Accepted Answer

There is a cricket team of 11 players is to be selected from 16 players, which must include 3 bowlers and a wicketkeeper.

there will be a team of 7 batsmen, 1 wicketkeeper and 3 bowlers.

there are 5 bowlers from which 3 is to be selected in ⁵C₃ ways

⇒there are two wicketkeepers out of which 1 is to be selected in²C₁

hence, from 9 players left 7 is to be selected from that in ¹¹C₇ ways.

by Multiplication principle , we get

= ⁵C₃ ²C₁ ⁹C₇

Applying ⁿC_r =

= 720 ways