Let f(n,k) be the number of k-subsets of an n set {1,2,....,n} that does not contain a pair of consecutive integers. Show that f(n,k)= {n-k+1} \choose {k} I know we can think of it as a sequence of k 1's and n-k 0's with no pair of consecutive 1's, but I can't figure out why this would be the same as choosing k places from n-k+1. Any help would be appreciated.