Question

Math

Posted 4 months ago

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You need to put your reindeer, Balthazar, Rudy, Jebediah, and Ezekiel, in a single-file line to pull your sleigh. However, Ezekiel and Jebediah 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?
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Answer from Sia

Posted 4 months ago

Solution by Steps

step 1

Consider Ezekiel and Jebediah as a single entity since they must be next to each other

step 2

There are now 4 entities to arrange: Balthazar, Rudy, the unnamed reindeer, and the Ezekiel-Jebediah pair

step 3

Calculate the number of arrangements for these 4 entities, which is $4!$

step 4

Recognize that within the Ezekiel-Jebediah pair, the two can be arranged in 2! ways

step 5

Multiply the arrangements of the 4 entities by the arrangements within the pair: $4! \times 2!$

step 6

Compute the product: $4! \times 2! = 24 \times 2 = 48$

Answer

There are 48 ways to arrange the reindeer.

Key Concept

Permutations with Constraints

Explanation

When a constraint requires two items to be together, treat them as a single entity and then multiply by the permutations within that entity.

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