You need to put your reindeer, Lancer, Prancer, Gloopin, and Bloopin, in a single-file line to pull your sleigh. However, Prancer and Lancer are fighting, so you have to keep them apart, or they won't fly.
How many ways can you arrange your reindeer?

This is for Permutations and Combinations.

P43=4!(4–3)!=241=24

Step-by-step explanation:

There are four choices you can make for the lead reindeer. For each possible choice, there are then three remaining you can choose to fly second, making 4×3=12 choices for the lead pair. For each possible choice there are two remaining reindeer to take up the back position, making 12×2=24 choices for the team of three.

This type of problem is called a permutation problem, and we write Pnr for the number of ways of choosing r items from n possibilities when the order of the items matters. In this case we are choosing 3 reindeer from 4 possibilities, and the order they appear in the flying line does matter, so the answer we want is P43. The general formula is Pnr=n!(n−r)!. For the answer we are looking for we therefore have:

P43=4!(4–3)!=241=24

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step-by-step explanation: