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

Monday, February 2nd, 2015


Rank of a Word in a dictionary with or without repetition

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 SBIPO.
With just 5 letters, total possible arrangements are 5! or 120. It is not practical to write all of them down and find out the rank of the word SBIPO.
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 B, I, O, P, S

Step 2: Find out the number of words that start with a superior letter
Any word starting from B will be above SBIPO. So, if we fix B at the first position, we can have 4! or 24 words.
Similarly, there will be 24 words that will start from I, 24 words that will start with O, and 24 words that will start with P.
So, total number of words that do no start with S and are above SBIPO is 4*24 = 96

Step 3: Solve the same problem, without considering the first letter
We need to find out the rank of BIPO
Correct order is B, I, O, P
=> BIPO will be the second word after BIOP
=> Overall rank of the word SBIPO is 96 + 2 = 98.

This might seem long but once you get a little bit of practice, you will be able to solve these questions in less than a minute.

Rank of a word – with repetition of letters

Let us consider the word IBPSPO. As you can see, the word P is occurring twice in it. The process remains the same as above. However, there will be a slight difference in the way we calculate the answer.

Step 1: Write down the letters in alphabetical order.
The correct order is B, I, O, P, P, S

Step 2: Find out the number of words that start with a superior letter
Number of words that start with B will be 5!/2! = 60 (we are dividing by 2 because P is repeating itself)

Step 3: Solve the same problem, without considering the first letter
We have to find the rank of BPSPO
This will be the same as the rank of PSPO
Words above PSPO are the three words starting from O (and ending with PPS, OPSP, OSPP)
Also, PPOS, PPSO, and PSOP will be above PSPO.
=> PSPO will be the 7th word in the list
=> BPSPO will be the 7th word in the list
=> Overall rank of the word IBPSPO is 60 + 7 = 67.

I hope that you found this post useful.

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