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

The alphabetical order of the letters in SACHIN is: A, C, H, I, N, S.Total number of letters = 6.Words starting with A: $5!=120$ Words starting with C: $5!=120$ Words starting with H: $5!=120$ Words starting with I: $5!=120$ Words starting with N: $5!=120$ Total words before starting with S = $120\times 5=600$.The next word (starting with S) in alphabetical order will be:S + (A, C, H, I, N in order) = SACHIN.So, the serial number is $600+1=601$.