There are 12 volleyball players in all in a c | vedclass

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Question

(D) Total number of players = $12$.Number of players to be selected for the team = $9$.Since the captain is fixed,we have already selected $1$ player.

Vedclass · Accepted Answer

$165$

Vedclass · Answer

(D) Total number of players = $12$.Number of players to be selected for the team = $9$.Since the captain is fixed,we have already selected $1$ player.Therefore,we need to select the remaining $9 - 1 = 8$ players from the remaining $12 - 1 = 11$ players.The number of ways to choose $8$ players from $11$ is given by the combination formula $^{n}C_{r} = \frac{n!}{r!(n-r)!}$.Number of ways = $^{11}C_{8} = ^{11}C_{11-8} = ^{11}C_{3}$.$^{11}C_{3} = \frac{11 	imes 10 	imes 9}{3 	imes 2 	imes 1} = 11 	imes 5 	imes 3 = 165$.Thus,the team can be formed in $165$ ways.

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?

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