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!×2Now, we simplify this expression. First, we factor out 8 ! from the expression:
9!−8!×2=8!(9−2)=8!×7The correct answer is:
Option B:
8!×‌