Question

Five men, two women, and a child sit around a table. Find the number of arrangements where the child is seated between the two women.

Answer 1

Five men, two women, and a child sit around a table.
Child is seated between the two women.
∴ The two women can be seated on either side of the child in 2! ways.
Let us consider these 3 (two women and a child) as one unit.
Also, these 3 are to seated with 5 men,
(i.e. total 6 units) which can be done in (6 − 1)! = 5! ways
∴Total number of arrangements if the child is seated between two women = 5! × 2!