Question

Four men, two women and a child sit at a round table. Find the number of ways of arranging the seven people if the child is seated:
i) Between these two women
ii) Between two men

Answer 1

$WCW\to 2!$ ways to arrange

$\downarrow$ women

considered as one number

Now we have total of $S$ members

$M,M,M,M,WCW$

So, Total ways $=4!\times 2!=48$

First select $2$ men nad then arrange $2$ men and a child between them.

${}^4{C}_2\times 2!$

Now arrange $5$ members

$M,M,W,W,MCM$

So, Total ways $=4!\times 2!\times {}^4{C}_2=288$