In how many ways can $4$ men and $3$ women be arranged at a round tale if:
i) the women always sit together?
ii) the women never sit together?
I attempted both the questions but the answers I got don't match the ones given in the source. This is what I did:
For (i) I considered the women to be one unit, who can be arranged in $3!$ ways, and so the total no. of units would be $5$, which we could arrange in $4!$ ways. So the total is $4! \cdot 3!$
For (ii), it would translate to women sitting in the $3$ spaces between men, so I considered the table as two separate ones where the men sit in $3!$ ways, and the women sit in $2!$ ways, so the total would be $3! \cdot 2!$
I'd like to know where my reasoning fell apart.
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