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Mathematics-Online lexicon:

Picking of Subsets

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The following table shows the number of possibilities to select $ k$ elements from a set containing $ n$ elements. To this end, it is essential to distinguish whether the order is to be taken into account or not (that is whether one considers ordered or unordered combinations) as well as whether repetitions are allowed or not (that is whether one element can be picked several times).

  ordered unordered
with repetitions $ n^k$ $ \displaystyle \binom{n+k-1}{k}$
without repetitions $ n(n-1)\cdots(n-k+1)$ $ \displaystyle \binom{n}{k}$
(Authors: Höllig/Knesch/Abele)

see also:

[Annotations] [Examples]
  automatically generated 6/11/2007