A school principal and his wife, along with three other teachers, are to be seated in a row. The principal and his wife must sit next to each other. Find the number of ways this can be done.

1. Problem Description

A school principal and his wife, along with three other teachers, are to be seated in a row. The principal and his wife must sit next to each other. Find the number of ways this can be done.

2. Solution Steps

There are a total of 5 people to be seated. The principal and his wife must sit together. We can treat the principal and his wife as a single unit.

First, consider the principal and his wife as one entity. So now we have 4 entities to arrange: (principal and wife), teacher 1, teacher 2, teacher

3. The number of ways to arrange these 4 entities in a row is $4! = 4 \times 3 \times 2 \times 1 = 24$.

Next, the principal and his wife can switch positions within their unit. So there are 2 possible arrangements for the principal and wife: (principal, wife) or (wife, principal). Therefore, there are 2 ways to arrange the principal and wife within their unit.

To get the total number of ways to arrange the 5 people with the given condition, we multiply the number of arrangements of the 4 entities by the number of arrangements within the principal-wife unit:

$24 \times 2 = 48$.

3. Final Answer

The number of ways this can be done is 48.