Question

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

Answer 1

If the reindeer do not fight, there are 5!=120 ways to line them up in a straight line.
Out of these, Bloopin and Rudy are together in 4!=24 times.  Similarly Rudy and Bloopin will be together 4!=24 times.  So the number of ways they are not together is 120-24-24=72 ways.

Answer 2

If Bloopin and Rudy are fighting, the reindeer do not fight, there are 72 ways that you can arrange your reindeer.

What are permutations?

The different arrangements which can be made out of a given number of objects by taking out some or all at a time are called permutations.

If Bloopin and Rudy are fighting, the reindeer do not fight,

then there are 5! = 120 ways

Out of these, Bloopin and Rudy are together in 4! = 24 times.  

Similarly, Rudy and Bloopin will be together 4! = 24 times.  

So the number of ways they are not together

120-24-24 = 72 ways.

Learn more about permutations;

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