Question

If the letters of the word $SACHIN$ are arranged in all possible ways and these words(with or without meaning) are written out as in dictionary, then the position of the word $SACHIN$ will be

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

Answer 1

The correct option is A $601$

Alphabets present in the word $SACHIN$ are $S,A,C,H,I,N$
alphabetical order of the letters present in the given word is $A,C,H,I,N,S$
If the word starts with the letter $A$ $\left(A\_\_\_\_\_\right)$ then the remaining $5$ position can be filled in $5!$ ways.
If the word starts with $C$ $\left(C\_\_\_\_\_\right)$then the remaining $5$ positions can be filled in $5!$ ways.
If the word starts with $H$ $\left(H\_\_\_\_\_\right)$then the remaining $5$ positions can be filled in $5!$ ways.
If the word starts with $I$ $\left(I\_\_\_\_\_\right)$then the remaining $5$ positions can be filled in $5!$ ways.
If the word starts with $N$ $\left(N\_\_\_\_\_\right)$then 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 $5\times 5!=600$ ways
i.e. $SACHIN$ is the ${601}^{th}$ word.