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Quantitative Aptitude

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Question

There are 12 volleyball players in all in a college, out of which a team of 9 players is to be formed. If the captain always remains the same, then in how many ways can the team be formed?

A

36

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B

108

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C

99

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D

165

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Solution

The correct option is D
165

Since, It is necessarily to choose captain, 1 is already chosen.

Players left $= 12 - 1 = 11,$ More players need to choose to form a team $= 9 - 1 = 8$

So now 11 players 8 are to be chosen.

Required number of ways = $^{11} C_{8} = 165.$

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