Let X1, ..., Xn be i.i.d. random variables having a distribution P ∈ P, where P is the family of distributions on R having continuous c.d.f.'s. Let T = (X(1), ..., X(n)) be the vector of order statistics. Show that, given T, the conditional distribution of X = (X1, ..., Xn) is a discrete distribution putting probability 1/n! on each of the n! points (Xi1 , ..., Xin ) ∈ Rn, where {i1, ..., in} is a permutation of {1, ..., n}; hence, T is sufficient for P ∈ P.