3 men and 4 women are seated at a round table. Find the number of possible arrangements if one particular woman must sit between 2 men.
My answer: (5-1)!2! but answer is 144
Hello, Punch!
3 men and 4 women are seated at a round table.
Find the number of possible arrangements
if one particular woman must sit between 2 men.
Since we have a round table, that woman can sit anywhere.
She will be flanked by two men.
There are 3 choices for the man on her right, 2 choices for the man on her left.
The remaining 4 people (one man, 3 women) can be seated in $\displaystyle 4!$ ways.
Therefore, there are: .$\displaystyle 3\cdot 2\cdot 4! \:=\:144$ arrangements.