For integers k and n such that 1≤k<n, let Ckn=k!(n−k)!n!. Then (k+1n−2k−1)Ckn is an integer<spanclass=′latex−bold′>(A)</span>for all k and n<spanclass=′latex−bold′>(B)</span>for all even values of k and n, but not for all k and n<spanclass=′latex−bold′>(C)</span>for all odd values of k and n, but not for all k and n<spanclass=′latex−bold′>(D)</span>if k=1 or n−1, but not for all odd values k and n<spanclass=′latex−bold′>(E)</span>if n is divisible by k, but not for all even values k and n