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 do we search the meaning in dictionary?

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

Always dictionary give meaning for English words in alphabetical order. That is, dictionary gives 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.

Example :

The letters of the word ZENITH are written in all possible orders. If all the words are written in a dictionary, what is the rank or order of the word ZENITH ?   

Solution :

No. of new words formed with the letters of the word

ZENITH  =  6!  =  720

Alphabetical order of the letters of the word ZENITH is

E, H, I, N, T, Z 

Dictionary gives meanings in the order starting with E, H and so on.

Number of words can be formed starting with E, H and so on.  

E  __  __  __  __  __  =  5!  =  120 words

H  __  __  __  __  __  =  5!  =  120 words

I  __  __  __  __  __  =  5!  =  120 words

N  __  __  __  __  __  =  5!  =  120 words

T  __  __  __  __  __  =  5!  =  120 words

Z  E  H  __  __  __  =  3!  =  6 words

Z E I  __  __  __  =  3!  =  6 words

Z E N H  __  __  =  2!  =  2 words

Z E N I H  __  =  1!  =  1 word

Z E N I T H  =  1!  =  1 word

Thus, the total Number of words is

=  120 + 120 + 120 + 120 + 120 + 6 + 6 + 2 + 1 + 1

=  616

So, the rank or order of the word ZENITH is 616.

Apart from the problems given on above, if you want to learn solving problems on permutation and combination, 

Please click here

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