COMEDK 2024 Shift 1 Paper

To solve this problem, we first need to calculate the total number of ways to arrange the letters in the word "CHRISTMAS" without any restrictions. The word "CHRISTMAS" consists of 9 distinct letters.
The total number of arrangements of 9 distinct letters is given by:
9 !
Next, we calculate the number of arrangements where the letters "C" and "M" are adjacent. To do this, we can treat the pair "CM" as a single unit. Thus, we have the following units to arrange: {CM,H,R,I,S,T,M,A,S}, which constitutes 8 units.
The number of ways to arrange these 8 units is:
8 !
To find the number of arrangements where " C " and " M " are not adjacent, we subtract the number of adjacent arrangements from the total number of arrangements:
9!−8!×2
Now, we simplify this expression. First, we factor out 8 ! from the expression:
9!−8!×2=8!(9−2)=8!×7
The correct answer is:
Option B:
8!×‌

7

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