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

There are 5 people in total: the principal, his wife, and three other teachers. Since the principal and his wife must sit together, we can consider them as a single unit.

Let's denote the principal as P, his wife as W, and the three teachers as T1, T2, and T

3. We can consider the principal and his wife as a single entity (PW or WP).

So, we have 4 entities to arrange: (PW), T1, T2, T

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 (PW or WP), so we must multiply by

2. The number of ways to arrange the principal and his wife is $2! = 2 \times 1 = 2$.

Therefore, the total number of arrangements is $4! \times 2!$.

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

3. Final Answer

The number of ways to seat the principal, his wife, and three other teachers such that the principal and his wife sit next to each other is 48.