Four married couples have bought eight seats in a row for a musical play. In how many ways can they be seated if each couple is to sit together with the wife to the left of her husband?

Question

Four married couples have bought eight seats in a row for a musical play. In how many ways can they be seated if each couple is to sit together with the wife to the left of her husband?

Answer 1

To solve this problem, we can treat each couple as a single entity and arrange these entities in a row. There are 4 couples, so we have 4 entities to arrange.

Step 1: Seat the first couple
Since the wife should be seated to the left of her husband, we have two options for the first couple: (wife, husband) or (husband, wife).

Step 2: Seat the remaining couples
For the remaining 3 couples, we can simply multiply the number of available seats by the number of couples remaining and keep multiplying for each couple. However, since the seats are adjacent, we can assume there is only one seat for each couple.

Step 3: Calculate the arrangements
For the first couple, there are 2 options. For the second couple, there is only 1 option since there are no other seats left. Similarly, for the third couple, there is only 1 option, and for the fourth couple, there is only 1 option.

Therefore, the total number of arrangements is: 2 * 1 * 1 * 1 = 2

Hence, there are 2 ways they can be seated.

Four married couples have bought eight seats in a row for a musical play. In how many ways can they be seated if each couple is to sit together with the wife to the left of her husband?

380

To solve this problem, we can treat each couple as a single entity and arrange these entities in a row. There are 4 couples, so we have 4 entities to arrange.