Question

Find the number of sitting arrangements for 3 men and 3 women to sit around a table so that exactly two women are together.

Answer 1

Two women sit together and one woman sits separately.
Woman sitting separately can be selected in 3 ways.
Other two women occupy two chairs in one way (as it is circular arrangement). They can be seated on those two chairs in 2 ways. Suppose two chairs are chairs 1 and 2 shown in the figure. Then the third woman has only two options viz chairs 4 or 5.
∴ Third woman can be seated in 2 ways. 3 men are seated in 3! ways
Required number = 3 × 2 × 2 × 3!
= 12 × 6
= 72