Imagine arranging 6 people to sit on a bench and 3 of them have to sit side by side. How many relevant arrangements will be made?

Step 1: Arrange the 4 blocks on the bench
Suppose the 3 people who must sit together are A, B, and C.
Since they must sit side by side, we treat them as a single block.
Now, instead of arranging 6 individuals, we are arranging 4 units: the ABC block and the 3 remaining people.
The number of ways to arrange these 4 blocks on the bench is 4! = 24.
Step 2: Arrange A, B, and C within their block
Within their block, A, B, and C can be arranged among themselves in 3! = 6 different ways.
So, for each of the 24 block arrangements, there are 6 possible internal arrangements of A, B, and C.
Therefore, the total number of valid arrangements is: 4! × 3! = 24 × 6 = 144.