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

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Question

(B) To select a team of $11$ players from $16$ players where $1$ particular player must always be excluded,we effectively need to choose $11$ players

Vedclass · Accepted Answer

$1365$

Vedclass · Answer

(B) To select a team of $11$ players from $16$ players where $1$ particular player must always be excluded,we effectively need to choose $11$ players from the remaining $15$ players $(16 - 1 = 15)$.This is calculated using the combination formula ${}^{n}C_{r} = \frac{n!}{r!(n-r)!}$.Here,$n = 15$ and $r = 11$.Number of ways = ${}^{15}C_{11} = {}^{15}C_{15-11} = {}^{15}C_{4}$.${}^{15}C_{4} = \frac{15 	imes 14 	imes 13 	imes 12}{4 	imes 3 	imes 2 	imes 1} = 15 	imes 7 	imes 13 = 1365$ ways.

In how many ways can a cricket team of $11$ players be selected out of $16$ players if $1$ particular player is to be excluded?

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