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?

Question

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?

Accepted Answer

∻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: $4! imes 2!$. ‖ ‖ step 6 ⋮ Compute the product: $4! imes 2! = 24 imes 2 = 48$. ‖ ∻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.◊What is the formula for calculating the number of ways to arrange objects, taking into account constraints?⍭ Generate me a similar question◊⚹

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