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If there are only a handful of objects, then you can count them with a moment's thought, but the techniques of combinatorics can extend to quickly and efficiently tabulating astronomical quantities. See more

Andy, Brandy, Candy and Dandy are 4 quadruplets.

How many ways are there to arrange them in a row (without any restriction)?

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Andy, Brandy, Candy and Dandy are 4 quadruplets.

Andy and Brandy are very friendly and want to sit next to each other. How many ways are there to arrange all 4 quadruplets in a row?

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Andy, Brandy, Candy and Dandy are 4 quadruplets.

Andy and Candy are quarreling with each other, and refuse to sit next to each other. How many ways are there to arrange them in a row?

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Andy, Brandy, Candy and Dandy are 4 quadruplets.

Andy and Candy are quarreling with each other, and refuse to sit next to each other.

Likewise, Brandy and Dandy are quarreling with each other, and refuse to sit next to each other.

How many ways are there to arrange them in a row?

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Andy, Brandy, Candy and Dandy are 4 quadruplets.

Andy and Brandy are quarreling with each other, and refuse to sit next to each other.

Andy and Candy are quarreling with each other, and refuse to sit next to each other.

How many ways are there to arrange them in a row?

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