It is required to seat 5 men and 4 women in a | vedclass

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(A) Total number of people $= 5$ men $+ 4$ women $= 9$ people.In a row of $9$ positions,the even places are the $2^{nd}, 4^{th}, 6^{th},$ and $8^{th}$

Vedclass · Accepted Answer

$2880$

Vedclass · Answer

(A) Total number of people $= 5$ men $+ 4$ women $= 9$ people.In a row of $9$ positions,the even places are the $2^{nd}, 4^{th}, 6^{th},$ and $8^{th}$ positions.There are $4$ even places available,and there are $4$ women to occupy these positions.Therefore,the number of ways to arrange the women in the even places is $P(4, 4) = 4! = 24$.There are $5$ remaining odd positions $(1^{st}, 3^{rd}, 5^{th}, 7^{th}, 9^{th})$ and $5$ men to occupy these positions.Therefore,the number of ways to arrange the men in the remaining positions is $P(5, 5) = 5! = 120$.By the fundamental principle of counting,the total number of arrangements is $P(4, 4) 	imes P(5, 5) = 4! 	imes 5!$.Total arrangements $= 24 	imes 120 = 2880$.

It is required to seat $5$ men and $4$ women in a row so that the women occupy the even places. How many such arrangements are possible?

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