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There are $n$ different types of objects and $k$ positions where an object can be placed. How can I determine the number of ways in which these $k$ positions can be filled by using objects of these $n$ types?

Any number of objects from a given type can be used and two objects of the same type are indistinguishable.

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  • $\begingroup$ In each position is there to be just one object ? $\endgroup$ Apr 15, 2016 at 10:59

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You have $n$ different options for each of $k$ positions, and they're all independent, so by the multiplication principle there are $n^k$ possibilities.

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