Another great explanation. Thank you Bunuel
subhashghosh wrote:
Hi
Could someone please help me with this, I am getting an answer 240. But I'm not sure if I'm correct.
Find the number of ways in which four men, two women and a child can sit at a table if the child is seated between two women.
Regards,
Subhash
Note:
The number of arrangements of n distinct objects in a row is given by \(n!\).
The number of arrangements of n distinct objects in a circle is given by \((n-1)!\).
We have M, M, M, M, W, W, C --> glue two women and the child so that they become one unit and the child is between women: {WCW}. Now, these 5 units: {M}, {M}, {M}, {M}, {WCW} can be
arranged around the table in (5-1)!=4! ways and the women within their unit can be arranged in 2 ways {W1, C, W2} or {W2, C, W1} so total # of arrangement is 4!*2=48.
Answer: 48.
240 would be the answer if the arrangement were in a row: {M}, {M}, {M}, {M}, {WCW} can be
arranged in a row in 5! ways and the women within their unit can be arranged in 2 ways {W1, C, W2} or {W2, C, W1} so total # of arrangement is 5!*2=240.
P.S.
Please read and follow: how-to-improve-the-forum-search-function-for-others-99451.html So please provide answer choices for PS questions.