In how many ways can 5 men and 2 women be sea | vedclass

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Question

(B) The total number of ways to arrange $7$ people ( $5$ men and $2$ women) around a circular table is $(7-1)! = 6! = 720$. To find the number of ways

Vedclass · Accepted Answer

$480$

Vedclass · Answer

(B) The total number of ways to arrange $7$ people ( $5$ men and $2$ women) around a circular table is $(7-1)! = 6! = 720$. To find the number of ways where the two women sit together,we treat the two women as a single unit. Now,we have $5$ men and $1$ unit of women,totaling $6$ entities. The number of ways to arrange $6$ entities around a circular table is $(6-1)! = 5! = 120$. Since the $2$ women can be arranged among themselves in $2! = 2$ ways,the total number of ways where the two women sit together is $120 	imes 2 = 240$. The number of ways where the two women do not sit together is the total number of arrangements minus the number of arrangements where they sit together: $720 - 240 = 480$.

In how many ways can $5$ men and $2$ women be seated around a circular table such that the two women do not sit together?

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