In how many ways can 4 men and 3 women be arranged in a round table: i) if the women always sit together? ii) if the women never sit together?
[Math] Seating arangement of 4 men and 3 women in a round table …
combinations
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Best Answer
For case $1$: First fix the women in one group. $3$ women can be seated in $3!$ ways. The $4$ men can be seated in the remaining $4$ places in $4!$ ways. Therefore, there are $144$ arrangements.
For case $2$: First fix the men in circular arrangement, which can be done in $3!$ following from the formula $(n-1)! $. Now there are $4$ places between the men and three women are to be seated between the men. That can be done in $^4 P_3$ ways. Again you get $144$ arrangements.
Hope it helps.