In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
Question:
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
Solution:
In the given word ASSASSINATION, the letter A appears 3 times, S appears 4 times, I appears 2 times, N appears 2 times, and all the other letters appear only once.
Since all the words have to be arranged in such a way that all the Ss are together, SSSS is treated as a single object for the time being. This single object together with the remaining 9 objects will account for 10 objects.
These 10 objects in which there are 3 As, 2 Is, and 2 Ns can be arranged in $\frac{10 !}{3 ! 2 ! 2 !}$ ways.
Thus, required number of ways of arranging the letters of the given word
$=\frac{10 !}{3 ! 2 ! 2 !}=151200$