Question

If the letters of the word ‘SACHIN’ are arranged in all possible ways and these words are written in dictionary order, then the word "SACHIN’ appears at serial number?

• A. $600$
• B. $601$
• C. $602$
• D. $603$

Answer 1

The correct option is B

$601$

Apply permutations to evaluate the required answer

The alphabetical order of the word ‘SACHIN’ is A, C, H, I, N, S.

The number of words starting with ‘A’ is $5!=120$.

The number of words starting with ‘C’ is $5!=120$.

The number of words starting with ‘H’ is $5!=120$.

The number of words starting with ‘I’ is $5!=120$.

The number of words starting with ‘N’ is $5!=120$.

The number of words starting with ‘SACHIN’ is $1$.

Thus the position of the word ‘SACHIN’ is $\left(120+120+120+120+120+1\right)=601$.

Hence, the position of the ‘SACHIN’ is $601$.