The number of ways of selecting 15 teams from | vedclass

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(A) To form $15$ teams,each consisting of one man and one woman from $15$ men and $15$ women:$1$. The first man can be paired with any of the $15$ wom

Vedclass · Accepted Answer

$15!$

Vedclass · Answer

(A) To form $15$ teams,each consisting of one man and one woman from $15$ men and $15$ women:$1$. The first man can be paired with any of the $15$ women in $15$ ways.$2$. The second man can be paired with any of the remaining $14$ women in $14$ ways.$3$. Continuing this process,the $15$th man can be paired with the last remaining woman in $1$ way.Therefore,the total number of ways to form the teams is the product of these choices:$= 15 	imes 14 	imes 13 	imes \dots 	imes 1 = 15!$Note: The original provided solution in the prompt was mathematically incorrect as it treated the selection as a sum of squares rather than a permutation of pairs.

The number of ways of selecting $15$ teams from $15$ men and $15$ women,such that each team consists of a man and a woman,is

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