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Question

There are 6 batsmen, 7 bowlers, and 2 wickets keepers. Find the number of ways of forming a team of 11 players having at least 4 batsmen, at least 5 bowlers, and at least 1 wicket keeper.


A

567

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B

525

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C

462

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D

777

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Solution

The correct option is D

777


Find the number of ways

Given, team size =11 players

Case 1: 5 batsmen, 5 bowlers, 1 wicket-keepers.

Number of ways

=C56×C57×C12=6×7!5!7-5!×2...(Cr=n!r!n-r!n)=6×7×6×5!5!×2×2=252

Case 2: 4 batsmen, 6 bowlers, 1 wicket-keepers.

Number of ways

=C46×C67×C12=6!4!6-4!×7×2...(Cr=n!r!n-r!n)=6×5×4!4!×2×7×2=210

Case 3: 4 batsmen, 5 bowlers, 2 wicket-keepers.

Number of ways

=C46×C57×C22=6!4!6-4!×7!5!7-5!×1...(Cr=n!r!n-r!,Cnn=1n)=6×5×4!4!×2×7×6×5!5!×2×1=315

Total number of ways =252+210+315=777

Hence option (D), 777 is the correct answer.


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