COMEDK · Maths · 4. Permutation Combination
In how many ways can the word "CHRISTMAS" be arranged so that the letters '\(\mathrm{C}\)' and '\(\mathrm{M}\)' are never adjacent?
- A \(9!\times \dfrac{7}{2}\)
- B \(8!\times \dfrac{9}{2}\)
- C \(8!\times \dfrac{7}{2}\)
- D \(7!\times \dfrac{9}{2}\)
Answer & Solution
Correct Answer
(C) \(8!\times \dfrac{7}{2}\)
Step-by-step Solution
Detailed explanation
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 \(\dfrac{9!}{2!}\). To find the number of arrangements where C and M are never adjacent, we subtract the arrangements where C and M are adjacent from…
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