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

ln a dictionary the words at each stage are arranged in alphabetical order. We must therefore consider the words beginning with A, C, H, I, N, Sin order. A will occur at first place as often as there are ways of arranging the remaining 5 letters all at a time i.e. A will occur at first place F times. 

Thus,

Number of words starting with $A=5!$

5irnilarly, N umber of words starting wi the $C=5!$

Number of words starting with $H=5!$

Number of words starting with $I=5!$

Number of words starting with $N=5!$

SCHIN appears in the list of words beginning with S. Cearly, itis the first word in the list of words beginning with S.SACHIN appears at serial number

(5! + 5! + .5! + 5! + 5! + 1) = 601