The number of ways in which 6 men and 4 women | vedclass

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(B) Total people $= 6 	ext{ men} + 4 	ext{ women} = 10 	ext{ people}$.First,calculate the total number of ways to seat $10$ people around a circula

Vedclass · Accepted Answer

$7 	imes 8!$

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(B) Total people $= 6 	ext{ men} + 4 	ext{ women} = 10 	ext{ people}$.First,calculate the total number of ways to seat $10$ people around a circular table,which is $(10-1)! = 9!$.Next,calculate the number of ways where a particular man and a particular woman sit adjacent to each other.Treat the particular man and woman as a single unit. Now we have $9$ units to arrange around a circular table,which can be done in $(9-1)! = 8!$ ways.Within the unit,the man and woman can be arranged in $2! = 2$ ways.So,the number of ways they sit together is $2 	imes 8!$.The number of ways they never sit adjacent is the total ways minus the ways they sit together:$9! - (2 	imes 8!) = (9 	imes 8!) - (2 	imes 8!) = (9 - 2) 	imes 8! = 7 	imes 8!$.

The number of ways in which $6$ men and $4$ women can be seated around a table so that a particular man and a particular woman never sit adjacent to each other is

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