Complicated Combinatorics Problem

In how many ways can a we arrange, in a row, six balls... when we have to choose from seven non-unique cricket balls, six non-unique tennis balls and five non-unique squash balls?

In total, 18 balls from three unique sets, each set of which contains non-unique entities, and each set is differently sized and one of which contains one fewer ball than we wish to arrange.

The answer is supposed to be 728, according to my reference. Im just not sure how to solve it. I could probably solve this by breaking it down into specific cases, and adding it all up... but Id might as well list each possible combination if Im going to do that. Im looking for a simpler method.