How to find Rank of a Word in Dictionary (With Repetition and Without Repetition)

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A very common type of question that gets asked in various banking and management entrance exams is based upon the concept of finding out the rank of a word. In this post, I will like to discuss the concept behind the same. Let us look at the two types.

Rank of a word – without repetition of letters

Suppose that you are given a word in which none of the letters are repeated and you asked to find out the rank of the word in a dictionary. For example, if the word which was given to you was CAT, it will be very easy to find out its rank. You will write down all possible combinations of the letters. Those are:
CAT,CTA, ATC, TCA, ACT, TAC

Now, you will arrange them in alphabetical order. It would become something like this:
ACT, ATC, CAT, CTA, TAC, TCA
CAT is third in the above list. So, the rank of the word CAT is 3.
But, as you might have realized by now – the problem would become extremely difficult if the word is bigger. Let us say that the word is Ganesh.
With just 6 letters, total possible arrangements are 6! or 720. It is not practical to write all of them down and find out the rank of the word Ganesh .
To solve questions like these, here is the process we need to follow.


Step 1: Write down the letters in alphabetical order.
The correct order will be A ,E ,G ,H ,N and S Rank them as alphabetical order  

Step 2: Find out the number of letters on the right with lower rank  As G is 3 letter in alphabetical order and there are 2 letters on the right side with lower rand than G so we write 2 as its value and A is ranked 1 and there is no letter on right side of A which is lower rank than A so value is 0 

Step 3: Write 0! from right end and continue till left end with increasing order 

Such as we start with 0! and reached 5! for first value.

Step 4: Multiply with respective value and get the answer.

240 + 0 + 12 + 0 + 2 + 0 =254



Word GANESH
ALPHABETICAL
ORDER
315264
RANKING ON RIGHT
LOWER THAN CURRENT 
202021
POSITION OF FACTORIAL5!4!3!2!1!0!
TOTAL RANK 240012020

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jitesh Gupta

HEAD MENTOR AT HEADACHE TUTORIALS 

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