Question

Two couples​ (Adam/Brenda and​ Carl/Darlene) have bought tickets for four adjacent seats to see a musical. In how many ways can the four people be seated if the couples do not sit together​?

Answer 1

Answer:

The correct answer is 8.

Step-by-step explanation:

Two couples have bought tickets for four adjacent seats to see a musical.

To find the number of ways can the four people be seated if the couples do not sit together​. This is equivalent to finding total number of ways subtract number of ways they are sitting together.

Total number of ways four people can sit in four chairs are 4! = 24.

Number of ways the at least one of the couples sit together is 3! × 2 + 4= 16.

Total number of ways in which the couples do not sit together is

24 - 16 = 8.

We can even think this way (alternate way of thinking):

There are four chairs _ _ _ _.

For the first chair there are four possible options, i.e anyone can sit; then for the second chair there are only two possible options, i.e the other couple; for the third chair there is 1 option, i.e the spouse of the first person who sat on the first chair ; and for the last chair there is only one person left. Thus the number of ways are 4 × 2 × 1 × 1 = 8.