Hello TulkiA well-known result states that the number of arrangements of items, where of the items are identical of the first kind, items are identical of the second kind, ... is . See, for example, just here.

So if we have items, which can be sorted into groups of , each group containing identical items, then the number of arrangements of the items is . This number is therefore an integer.

To generalise this, the same argument applies if , for any positive integer , whereby is therefore also an integer.

Grandad