Question

A cricket team of 11 players is to be formed from a pool of 16 players that includes 4 bowlers and 2 wicket-keepers. In how many different ways can a team be formed so that the team has at least 3 bowlers and wicket keeper?

• A. 2472
• B. 2274
• C. 2427
• D. 1236

Answer 1

Answer: (A)

2472

Answer 2

Number of different ways so that the team has at least 3 bowlers and wicket keeper,

$4C_32C_110C_7+4C_42C_110C_6+4C_32C_210C_6+4C_42C_210C_5$

= 4 x 2 x 120 + 1 x 2 x 210 + 4 x 1 x 210 + 1 x 1 x 252

= 960 + 420 + 840 + 252

= 2472

Hence, option A is the correct answer.The correct option is (A): 2472