In how many ways can a team of 10 players be | vedclass

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Question

(C) Total players available = $22$.Team size required = $10$.Since $6$ particular players must always be included,we have already selected $6$ players

Vedclass · Accepted Answer

$^{12}C_4$

Vedclass · Answer

(C) Total players available = $22$.Team size required = $10$.Since $6$ particular players must always be included,we have already selected $6$ players. Remaining spots to be filled = $10 - 6 = 4$.Since $4$ particular players must always be excluded,these players are removed from the pool of available players.Remaining players to choose from = $22 - 6 (	ext{included}) - 4 (	ext{excluded}) = 12$.We need to choose $4$ players from the remaining $12$ players.The number of ways to do this is given by the combination formula $^{n}C_{r} = \frac{n!}{r!(n-r)!}$.Number of ways = $^{12}C_{4} = \frac{12!}{4!8!} = \frac{12 	imes 11 	imes 10 	imes 9}{4 	imes 3 	imes 2 	imes 1} = 495$.Thus,the correct option is $C$.

In how many ways can a team of $10$ players be selected from $22$ players if $6$ particular players are always to be included and $4$ particular players are always excluded?

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