Six people are planning to see the Nut Cracker How many ways

Six people are planning to see the Nut Cracker. How many ways can you seat all six people if: Each is willing to take any seat. Two of the six insist on sitting together. The six people consist of three married couples and each wants to together with the husband seated on the left. Two of the six do not like each other and do not want to be seated side-by-side.

Solution

c) if there are 3 couples in 6 people. Consider this as there are only 3 people need to be seated in 3 empty seats.

This can be done in 3! ways = 6 ways

d) Let us consider 2 of them who do not like each other has to be together

This arrangement can be done in 5! * 2! ways

There are total 6! arrangements.

Hence, required arrangements are = 6! - 5! * 2!

= 480 ways