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

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

Permutations and Combinations

Solution:

In SACHIN order of alphabets is $A, C, H, I, N, S$
Number of words starting with $A = 5\, !$
Similarly for $C, H, I, N$. Now words start with $S$ and after that ACHIN are in ascending orders of position.
$\therefore $ $5(5 \,!)=600$ words are in dictionary before words with $S$ start and position of this word is $=601$.