Question

You need to put your reindeer, Gloopin, Balthazar, Bloopin, Prancer, and Quentin, in a single-file line to pull your sleigh. However, Prancer and Balthazar are best friends, so you have to put them next to each other, or they won't fly. How many ways can you arrange your reindeer?

a. 24
b. 48
c. 60
d. 120

Answer 1

The reindeer can be arranged in 48 different ways by considering Prancer and Balthazar as a single unit and then multiplying the number of arrangements for 4 units (24) by the number of ways to arrange Prancer and Balthazar within that unit (2), resulting in 48 (24*2).

Step-by-step explanation:

To determine how many ways we can arrange the reindeer Gloopin, Balthazar, Bloopin, Prancer, and Quentin in a single-file line with Prancer and Balthazar next to each other, we need to consider Prancer and Balthazar as a single unit because they need to be together. The question then becomes similar to arranging 4 units: (Prancer+Balthazar), Gloopin, Bloopin, and Quentin.

There are 4! (factorial of 4) ways to arrange these 4 units, which equals 24. However, since Prancer and Balthazar can be rearranged among themselves in 2! (factorial of 2) ways, we need to multiply our first result by 2. Therefore, we get 24 * 2 = 48 possible arrangements.

So, the answer is b. 48 ways to arrange the reindeer.