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?

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 in ²C1

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

⇒ By Multiplication principle, we get

= 5C3      2C1      9C7

= 720 ways