In how many ways can a cricket team of 11 pla | vedclass

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(A) Total players available = $16$.We need to select a team of $11$ players.Given conditions:$1$. $2$ particular players must be included.$2$. $1$ par

Vedclass · Accepted Answer

$715$

Vedclass · Answer

(A) Total players available = $16$.We need to select a team of $11$ players.Given conditions:$1$. $2$ particular players must be included.$2$. $1$ particular player must be rejected.Since $2$ players are already included,we need to select $11 - 2 = 9$ more players.Since $1$ player is rejected and $2$ are already included,the number of players remaining to choose from is $16 - 2 - 1 = 13$.Therefore,the number of ways to select the remaining $9$ players from $13$ players is given by the combination formula ${}^{n}C_{r} = \frac{n!}{r!(n-r)!}$.Number of ways = ${}^{13}C_{9} = {}^{13}C_{13-9} = {}^{13}C_{4}$.${}^{13}C_{4} = \frac{13 	imes 12 	imes 11 	imes 10}{4 	imes 3 	imes 2 	imes 1} = 13 	imes 11 	imes 5 = 715$.

In how many ways can a cricket team of $11$ players be selected out of $16$ players if $2$ particular players are to be included and $1$ particular player is to be rejected?

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