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Question 53

A cricket team of 11 players is to be formed from 20 players including 6 bowlers and 3 wicket keepers. The number of ways in which a team can be formed having exactly 4 bowlers and 2 wicket keepers is

Solution

There are 6 bowlers, 3 wicket keepers and 11 batsman in all. The number of ways in which a team of 4 bowlers, 2 wicket keepers and 5 batsman can be chosen

= $$C^6_4\times C^3_2\times C^{11}_5$$

= $$(\frac{6\times5}{1\times2})\times(\frac{3\times2}{1\times2})\times(\frac{11\times10\times9\times8\times7}{1\times2\times3\times4\times5})$$

= $$15\times3\times462=20790$$

=> Ans - (A)

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