Question

Among $14$ players, $5$ are bowlers. In how many ways a team of $11$ may be formed with at least $4$ bowlers?

• A. $265$
• B. $275$
• C. $264$
• D. $263$

Answer 1

The correct option is C $264$

There are $14$ players out of which $5$are bowlers.

A team of $11$ players have to be selected such that at least $4$ bowlers are included in the team.

Therefore, required number of ways

$={}^5{C}_4\times {}^9{C}_7+{}^5{C}_5\times {}^9{C}_6$

Required number of ways

$=\frac{5!}{4!1!}\times \frac{9!}{7!2!}+1\times \frac{9!}{6!3!}=180+84=264$

Hence, the option (C) is correct.