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Question

In a touring cricket team there are 16 players in all including 4 bowlers and 2 wicket-keepers, How many teams of 11 players from these, can be chosen , so as to include three bowlers and one wicket-keeper

A
650
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B
720
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C
750
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D
800
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Solution

The correct option is D 720
Thereare4bowlers2wicketkeepers10nonbowlersnotwicketkeepers.CaseAThereareexactly3bowlers,exactly1wicketkeeper,and7nonbowlersnonwicketkeepers.3C1×2C1×10C7=960CaseBThereareexactly4bowlers,exactly2wicketkeeper,and6nonbowlersnonwicketkeepers.4C3×2C2×10C6=840CaseCThereareexactly4bowlers,exactly1wicketkeeper,and6nonbowlersnonwicketkeepers.4C4×2C1×10C6=420CaseDThereareexactly4bowlers,exactly2wicketkeeper,and5nonbowlersnonwicketkeepers.4C4×2C2×10C5=252Now,Totalnumbersofways=960+840+420+252=2472Hence,totalnumberofwaysis2472.
Hence,option B is the correct answer.

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