Freeflows

Wombat Seating Arrangements

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?

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$\frac{a}{b}$
.
0
=
%

$a^n$
$a^{\circ}$
$a_n$
$\sqrt{}$
$\sqrt[n]{}$
$\pi$
$\ln{}$
$\log$
$\theta$
$\sin{}$
$\cos{}$
$\tan{}$

$($
$)$
$[$
$]$
$\cap$
$\cup$
$,$
$\infty$

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

$\dfrac{7!\phantom{}}{3!\phantom{}}=\boxed{840}$ ways.

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