Order matters | Order does not matter | |
With repetitions | n^{k} | |
Without repetitions |
Because the number of all subsets of an n-set,
whatever their cardinal
is 2^{n}, we have :
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.