In how many ways can the word "CHRISTMAS" be arranged so that the letters ' C ' and ' M ' are never adjacent?

Step-by-step solution

The word CHRISTMAS contains 9 letters: C, H, R, I, S, T, M, A, S. The letter S repeats twice. The total number of arrangements is 9! 2! . To find the number of arrangements where C and M are never adjacent, we subtract the arrangements where C and M are adjacent from the total number of arrangements. Treating (CM) as a single unit, we have 8 units: (CM), H, R, I, S, T, A, S. The number of arrangements of these 8 units is 8! 2! . Since C and M can be arranged as CM or MC, we multiply by 2!. Number of arrangements wh