In how many ways can a football team of 11 pl | vedclass

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Question

(C) Part $1$: Number of ways to select $11$ players out of $15$ is given by $C(15, 11)$.$C(15, 11) = C(15, 4) = \frac{15 	imes 14 	imes 13 	imes 12

Vedclass · Accepted Answer

$1001$

Vedclass · Answer

(C) Part $1$: Number of ways to select $11$ players out of $15$ is given by $C(15, 11)$.$C(15, 11) = C(15, 4) = \frac{15 	imes 14 	imes 13 	imes 12}{4 	imes 3 	imes 2 	imes 1} = 1365$.Part $2$: If a particular player must be included,we have already selected $1$ player. Now,we need to select the remaining $10$ players from the remaining $14$ players.This is given by $C(14, 10)$.$C(14, 10) = C(14, 4) = \frac{14 	imes 13 	imes 12 	imes 11}{4 	imes 3 	imes 2 	imes 1} = 1001$.Thus,the number of ways a particular player is included is $1001$.

In how many ways can a football team of $11$ players be selected from $15$ players? In how many cases can a particular player be included?

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