Teddy, Becky, and Jose are going to sit on a bench to wait for the bus. How many different arrangements can they sit on the bench so that Becky and Jose are sitting next to each other?

Answer 1

To solve this problem, we can consider Becky and Jose as a single entity. Let's call this entity BJ.

Now, we have three entities: Teddy, BJ, and the empty seat. We can arrange these three entities in three different ways:

1. Teddy - BJ - (Empty seat)
2. BJ - Teddy - (Empty seat)
3. (Empty seat) - BJ - Teddy

However, within the BJ entity, Becky and Jose can switch positions. Thus, we need to consider the possible arrangements within the BJ entity.

Becky and Jose can be arranged in two ways:

1. Becky - Jose
2. Jose - Becky

Therefore, the total number of different arrangements is 3 (possible arrangements of the entities) multiplied by 2 (possible arrangements within the BJ entity).

So, there are 3 x 2 = <<3*2=6>>6 different arrangements.