How to Find the Rank of a Word in Dictionary With Repetition ?
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.
Question 1 :
Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?
Solution :
The given string "THING" has 5 letters, there is no repetition of letters.
So, the number of strings can be made using the above 5 letters,
T, H, I, N, G = 5! = 120.
Now we have to find the word in the 85th place. For that let us count the words that can be formed using the letters
Alphabetical order of the word G, H, I, N, T
Number of words formed starting with "G"
G __ __ __ __ = 4! = 24
Number of words formed starting with "H"
H __ __ __ __ = 4! = 24
Number of words formed starting with "I"
I __ __ __ __ = 4! = 24
So far, we get 72 words. Hence the required word starts with the letter N.
Number of words starting with the letters "NG"
N G __ __ __ = 3! = 6
Number of words starting with the letters "NI"
N I __ __ __ = 3! = 6
So far, we get 84 words.
By writing the letters after N I in alphabetical order, we get the word "NIGHT".
Hence it must the required word at the 85^{th} place.
Question 2 :
If the letters of the word FUNNY are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, find the rank of the word FUNNY.
Solution :
Alphabetical order of the word "FUNNY"
F, N, N, U, Y
Number of words starting with "FN"
F N __ __ __ = 3! = 6
Number of words starting with "FUN". By arranging the remaining letters in the alphabetical order, we get
F U N N Y = 1
Hence the rank of the word "FUNNY" is 7.
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