If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number:

If the word started with the letter A then the remaining 5 positions can be filled in 5! Ways.
If it started with c then the remaining 5 positions can be filled in 5! Ways.
Similarly if it started with H, I, N the remaining 5 positions can be filled in 5! Ways.
If it started with S then the remaining position can be filled with A, C, H, I, N in alphabetical order as on dictionary.
The required word SACHIN can be obtained after the 5 × 5! = 600 Ways.
i.e. SACHIN is the 601^th word.