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

Explanation

`:'` There are 5 bowlers in 17 players.
Therefore, remaining players `= 17 =- 5 = 12`
No. of ways of selecting 4 bowelers out of 5 bowlers
`= .^(5)C_(4) = (5!)/(4!1!) = 5`
Again, no. of ways of selecting remaining 7 players out of remaining 12 players.
`= .^(12)C_(7) = (12!)/(7!5!)`
`= (12 xx 11 xx 10 xx 9 xx 8 xx 7!)/(5xx 4xx xx 2 xx 1 xx 7!) = 792`
Therefore, total no. of cricket eleven
`= 5 xx 792 = 3960`