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 $={ }^{5} C_{4} \times{ }^{9} C_{7}+{ }^{5} C_{5} \times{ }^{9} C_{6}$
$=180+84$
$=180+84$
$=264$