In how many ways can the letters of the word ASSASSINATION be arranged so that all the S s are together ?

Explanation

Total no of letters in the word ASSESSINATION = 13
In which 3A,4S,2I and 2N are included and remaining are different.
`:'` Four S are together then taking them as one letter, we have to arrange total 10 letters include this one letter and 9 other letters which include 3A,2I and 2N.
Then number of permutation
`=(lfloor10)/(lfloor2 xx lfloor2 xx lfloor3) = (10 xx 9 xx 8 xx 7 xx 6 xx 5 xx 4 xx lfloor3)/(2 xx 1 xx 2xx 1 xx lfloor3)`
`= 10 xx 9 xx 8 xx 7 xx 6 xx 5 = 151200`
Therefore, required number of ways = 151200