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:
The word ASSASSINATION consists of 13 letters including three As, four Ss, two Ns and two Is.
Considering all the Ss are together or as a single letter, we are left with 10 letters. Out of these, there are three As, two Ns and two Is.
Number of words in which all the Ss are together = Permutations of 10 letters of which three are similar to the first kind, two are similar to the second kind and two are similar to the third kind $=\frac{10 !}{2 ! 2 ! 3 !}=151200$