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 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?
Updated On: Sep 26, 2024
- 2472
- 2274
- 2427
- 1236
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The Correct Option is A
Solution and Explanation
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
\(4C_32C_110C_7+4C_42C_110C_6+4C_32C_210C_6+4C_42C_210C_5\)
= 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
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