Given: 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers

There are 5 players how can bowl, and we require 4 bowlers in a team of 11

∴ No. Of ways in which bowlers can be selected are: ⁵C₄

Now other players left are: 17 – 5(bowlers) = 12

Since we need 11 players in a team and already 4 bowlers are selected, we need to select 7 more players from 12.

∴ No. Of ways we can select these players are: ¹²C₇

∴ Total number of combinations possible are : ⁵C₄ × ¹²C₇

⇒ ⁵C₄ × ¹²C₇ =

⇒⁵C₄ × ¹²C₇ =

∴ Number of ways we can select a team of 11 players where 4 players are bowlers from 17 players are: 3960