jmc

Question

There are seven wombats in a council. Three of them are hairy-nosed wombats, while the rest are all different species. If the hairy-nosed wombats are indistinguishable but the other wombats are, how many ways can the wombats seat themselves in a row?

Accepted Answer

There are 7! ways to arrange all the wombats. However, because the order of the hairy-nosed wombats does not matter, we've overcounted by the number of ways to arrange those three wombats, or 3!. The answer is 7!3!=840 ways.