How Many Ways Can Santa Arrange His Reindeer?

How many ways can Santa arrange his reindeer?

As of this writing, it is the middle of summer in our part of the world, but Christmas is just around the corner. That is if you define “just around the corner” as 160 days from now.

We know the names of the reindeer are Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donner, Blitzen, and Rudolph. We also know that Rudolph has the important role of being the leading reindeer. In terms of how his fellow sleigh-pullers go, however, we are not told.

One of Santa’s biggest tasks during the summer months is making sure his reindeer are in shape for their busiest day of the year. One thing that is very important for him is to place the reindeer in just the right position when they begin pulling his sleigh. If all of the strongest reindeer are on one side, the sleigh could go off course. If the weakest ones are up front, they will slow down the ones attached in the rear.

When assigning his reindeer to their positions, Santa has a lot of options. Assuming that Rudolph’s place at the head of the sleigh is non-negotiable, there are 40,320 ways in which Santa can arrange the other eight reindeer.

If it is a particularly clear night, and Santa doesn’t need Rudolph’s shiny nose at the head of the pack, he has 362,880 possible combinations to choose from.

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