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Let us imagine that we have empty boxes to fill, and of them must be filled from a fixed set of items.
The first of these items can go in any one of the boxes; the next in any one of the remaining boxes; and so on. The number of ways of filling the first boxes from the fixed set is therefore
There are now remaining boxes to be filled with items to be chosen from the remaining . This can clearly be done in ways.
So I reckon the total number of ways is