Question

All the six letters of the name SACHIN are arranged to from different words without repeating any letter in any one word.The words so formed are then arranged as in a dictionary. What will be the Position of the world SACHIN in that sequence?

• A. $436$
• B. $590$
• C. $601$
• D. $751$

Answer 1

The correct option is C $601$

If the word started with the letter A then the remaining $5$ positions can be filled in $5!$ Ways

Similarly, for the other letters

No. of word starts with $A=5!$

No. of word starts with $C=5!$

No. of word starts with $H=5!$

No. of word starts with $I=5!$

No. of word starts with $N=5!$

Total words $=5!+5!+5!+5!+5!=5(5!)=600$

Next when words starting with $S$ appears, $SACHIN$ itself will be the $1^{st}$ word as $ACHIN$ are all in dictionary order,

Now add the rank of $SACHIN.$

So rank is $600+1=601$