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

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) 263

(c) 264

(d) 275

Solution:

(c) 264

Among 14 players, 5 are bowlers.

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

$\therefore$ Required number of ways $={ }^{5} C_{4} \times{ }^{9} C_{7}+{ }^{5} C_{5} \times{ }^{9} C_{6}$

$=180+84$

$=180+84$

$=264$