k-means is a data mining algorithm useful for clustering purposes:
Given K equally sized clusters, the probability that a randomly chosen initial centroid will come from any given cluster is 1/K, but the probability that each cluster will have exactly one initial centroid is much lower. (It should be clear that having one initial centroid in each cluster is a good starting situation for K- means.) In general, if there are K clusters and each cluster has n points, then the probability, p, of selecting in a sample of size K one initial centroid from each cluster is given by:
number of ways to select one centroid from each cluster$/$number of ways to select K centroids is equal to $ K!n^{ K}$ $/$ $(Kn)^{K}$
But i do not get how can we arrive at that formula?
Shouldn't it be the combination of k different items from the k different clusters?