Question 68

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?

Solution

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

= $$4_{C_{3}}2_{C_{1}}10_{C_{7}} + 4_{C_{4}}2_{C_{1}}10_{C_{6}} + 4_{C_{3}}2_{C_{2}}10_{C_{6}} + 4_{C_{4}}2_{C_{2}}10_{C_{5}}$$

= 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.

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