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### More about k-subsets 10/9

Summary of taking k elements out of n:
 Order matters Order does not matter With repetitions nk Without repetitions

Because the number of all subsets of an n-set, whatever their cardinal is 2n, we have :

Thus

On the other hand each term of this sum is smaller than the largest one, which is:

which is thus larger than their average:

Another way of considering the numbers of ways of choosing k sets out of n sets, with repetitions allowed is the number of ways of dropping k balls into n boxes, this image is an image often used in statistical mechanics. As I pointed out in class, there are several ways of putting probabilities on these spaces.

Susan Holmes
1998-12-07