Question

In a cricket board, Anil Jain is a cricket team selector. He can select a cricket team, 11 from 17 players in which only 5 players can bowl.

In how many ways exactly 4 bowlers must include out of 11 players?

Answer 1

Given that, total number of players is 17.
We have to select 11 players including exactly 4 bowlers.
Hence. 4 bowlers will be selected from 5 bowlers and remaining 7 players will be selected from 12 batsmen.
Now, 4 bowlers out of 5 bowlers can be selected in ${}^5{C}_4$, ways
7 Players out of 12 players can be selected in ${}^{12}{C}_7$ ways.

$\therefore$ Total number of ways selecting 11 players

${=}^5{C}_4{\times }^{12}{C}_7{=}^5{C}_4{\times }^{12}{C}_5$

$=5\times \frac{12!}{7!5!}=5\times \frac{2\times 11\times 10\times 9\times 8}{5\times 4\times 3\times 2\times 1}$

Hence, he can select the team of 11 players in 3960 ways.