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Question
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 word is THING
Arranging the letters of the word in the dictionary order
We have G, H, I, N, T
The number of strings that can be made using all the letters T, H, I, N, G of the word
THING is = 5! = 120
The number of words beginning with G = 4!
The number of words beginning with H = 4!
The number of words beginning with I = 4!
Number of words so far formed = 4! + 4! + 4!
= 24 + 24 + 24
= 72 words
As the required word is in the 85th position
The required word must begin with N
Number of words beginning with NG = 3!
A number of words beginning with NH = 3!
Total number of words so far formed
= 72 + 3! + 3!
= 72 + 6 + 6
= 84 words
The next string is the required string.
It should begin with NI and its first word beginning with NI which is NIGHT
∴ 85th strings are NIGHT.
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