RANK FINDING IN DICTIONARY PROBLEMS

About the topic "Rank finding in dictionary problems"

For some students "Rank finding in dictionary problems" is a difficult topic in quantitative aptitude. Actually it is not like that. Once we understand the concept, it is not a difficult one to understand. Even though there are many websites which explain this topic, students find it difficult to understand what has been explained in those websites. On this webpage, our team of experts give step by step explanation to find rank or order of a word in dictionary.

Rank finding in dictionary problems

Rank finding in dictionary problems starts with searching  a particular English word in dictionary.

For example, we want to know meaning of a particular word in English, say "DEVELOPMENT".  We will search the word in dictionary to get meaning of the word.

How will we search the meaning in dictionary?

In dictionary, we will go to the page where the words start from the alphabet "D". There we will search the word "DEVELOPMENT".

Always dictionary give meaning for English words in alphabetical order. That is, dictionary give meanings for the words starting with "A" at first. Then B, C and so on.

In dictionary, before the word "DEVELOPMENT", there would be so many words. starting with the alphabets A, B, C & D.

For example, in dictionary there are 1256 words starting with A, B, C &D before the word "DEVELOPMENT". The word DEVELOPMENT  comes at the position of 1257. So the rank of the word "DEVELOPMENT" is 1257.

So, "Rank finding in dictionary problems" is nothing but finding the position of the word in dictionary. That is, in what serial number the word comes in dictionary.

Steps involved in solving "Rank finding in dictionary problems"

Let us look at an example problem to understand "Rank finding in dictionary problems"

Problem:

The Letters of the word "ZENITH" are written in all possible orders. If all these words are written out as in a Dictionary, what is the rank of the word "ZENITH" ?

Step 1 :

First let us find the number of all possible orders in which the letters of the word "ZENITH" can be written.

That is no. of possible words with the letters of the word "ZENITH"

In the word "ZENITH", we have six letters and all of them are different.

No. of words can be formed  =  6!  =  6x5x4x3x2x1 =  720   

So, we can form 720 words with the letters of the word "ZENITH".

Step 2 :

Target of the question : Now, if all these words are written in a dictionary, where will the word "ZENITH" come?

Step 3 :

Let us write the letters of the word "ZENITH" in alphabetical order.

That is,  E, H, I, N, T, Z

When we write the 720 words in dictionary, we will have the words starting with "E" at first. Then H, I, N, T & Z. 

Our word "ZENITH" starts  with "Z". Clearly the word "ZENITH" will come after all the words starting with E, H, I, N, & T.

Because, dictionary will give meaning for the words in alphabetical order.

Step 4 :

Since dictionary gives meaning for the words in alphabetical order, it will first give meaning for the words starting with "E". 

The words starting with "E" will be in the form of  

                                       E, __ , __ , __ , __ , __ 

In the above form, there are six positions. Since the words start with "E", first position is filled by "E" and the remaining 5 positions will be filled by  H, I, N, T & Z. 

It can be done in 5! ways. And 5! = 120

So, number of words starting with "E" = 120

Step 5 :

The above 120 words starting with "E" will come before the words  staring with H, I, N, T & Z.

Now, dictionary will give meaning for the words starting with "H".

The words starting with "H" will be in the form of  

                                       H, __ , __ , __ , __ , __ 

In the above form, there are six positions. Since the words start with "H", first position is filled by "H" and the remaining 5 positions will be filled by  E, I, N, T & Z. 

It can be done in 5! ways. And 5! = 120

So, number of words start with "H" = 120

In the same way,

Number of words starting with "I"  = 120

Number of words starting with "N" = 120

Number of words starting with "T"  = 120

Step 6 :

 Number of words starting with "E" =  120 ----------(1)

 Number of words starting with "H" =  120 ----------(2)

 Number of words starting with "I" =  120 ----------(3)

 Number of words starting with "N" =  120 ----------(4)

 Number of words starting with "T" =  120 ----------(5)

(1) + (2) + (3) + (4) + (5) = 120 + 120 + 120 + 120 + 120 = 600

There are 600 words staring with E, H, I, N, T.

All these 600 words will come in dictionary before the words starting with "Z".

Step 7 :

Now, let us find the words starting with "Z".

Since we start with "Z", the first position will be filled by "Z" and the remaining positions will be filled by the letters E, H, I, N, T in alphabetical order as given below. 

(The list of words given below as per the dictionary order)

Z, E, __ , __ , __ , __   ----------- 4!  = 4x3x2x1 = 24 words

Z, E, H, __ , __ , __    ------------3!   = 3x2x1 = 6 words

Z, E, I, __ , __ , __    ------------3!   = 3x2x1 = 6 words

Z, E, N, H , __ , __    ------------2!   = 2x1 = 2 words

Z, E, N, H , __ , __    ------------2!   = 2x1 = 2 words

Z, E, N, I, H, T          ---------------- = 1 word 

Z, E, N, I, T, H           ---------------- = 1 word 


Step 8 :

To complete the task of rank finding in dictionary problems, let us summarize the words formed with the letters E, H, I, N, T, Z in alphabetical order.

 E, __ , __ , __ , __ , __  ---------------- = 5! = 120 words

 H, __ , __ , __ , __ , __  ---------------- = 5! = 120 words

 I, __ , __ , __ , __ , __  ---------------- = 5! = 120 words 

 N, __ , __ , __ , __ , __  ---------------- = 5! = 120 words

 T, __ , __ , __ , __ , __  ---------------- = 5! = 120 words

 Z, E, H, __ , __ , __    ------------3!   = 3x2x1 = 6 words

 Z, E, I, __ , __ , __    ------------3!   = 3x2x1 = 6 words

 Z, E, N, H , __ , __    ------------2!   = 2x1 = 2 words

 Z, E, N, I, H, T          ---------------- = 1 word 

 Z, E, N, I, T, H           ---------------- = 1 word 

When we add the number of words mentioned above starting from "E" to "ZENITH", we get  616 words.

That is, ZENITH comes at the place of 616.

Hence the rank or order of the word "ZENITH" is 616

After having seen the steps of the problem above, we hope students can do any question on "Rank finding in dictionary problems".

And also we hope that the students here after will not find it difficult to do problems on "Rank finding in dictionary problems"

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