A school principal, his wife, and 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, his wife, and 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

Let's consider the principal and his wife as a single unit.

Then, we have this unit and three other teachers to arrange.

This gives us a total of 4 entities to arrange: (principal and wife), teacher 1, teacher 2, teacher

3. These 4 entities can be arranged in $4!$ ways.

$4! = 4 \times 3 \times 2 \times 1 = 24$

However, the principal and his wife can switch places within their unit. The principal can sit to the left of his wife, or the wife can sit to the left of the principal. So there are 2 ways to arrange them within their unit.

Therefore, the total number of ways to arrange the principal, his wife, and the three teachers such that the principal and his wife are next to each other is $4! \times 2$.

$4! \times 2 = 24 \times 2 = 48$

3. Final Answer

48