The number of ways of writing the letters of $'ASSASSIN'$ in a row so that no two $S$ come together is

The word ASSASSIN has 8 letters, featuring 4 S letters and 4 non-S letters (A, A, I, N). First arrange the 4 non-S letters, which can be done in 4 factorial divided by 2 factorial ways, equaling 12; this creates 5 gaps (including the ends) to place the S letters so none touch. The 4 S letters can be arranged in these 5 gaps in 5P4 ways, which equals 120. The total number of valid arrangements is 12 multiplied by 5, which equals 60.

• Thanks
• Wrong explanation