5) Let I < m < n be two integers and let X(m,n) be the set of subsets of I, 2, ..., n of size m. For example, X(2,3) = {{1,2},{1,3},{2,3}}. We define an action of Sn on X(m,n) by a(i1,...,im) = {a(i1),a(i2),...,a(im)}, for a ∈ Sn. Prove that the action is transitive and that the stabilizer of a point is isomorphic to Sm x Sn-m.