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# If the letters of the word KRISHNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISHNA isA. 324B. 341C. 359D. None of these

Last updated date: 09th Sep 2024
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Hint: In this problem, first you calculate the number of words starting from A then The number of words starting from I similarly, The number of words starting from KA, The number of words starting from KI, The number of words starting from KN, The number of words starting from KRA, The number of words starting from KRIA, The number of words starting from KRIN, The number of words starting from KRISA, The number of words starting from KRISNA and after that we can calculate the rank of word ‘KRISNA’.

We will follow the alphabetic order from top to bottom and will find the number of words that come before KRISHNA.
The number of words starting from A are $= 5! = 120$
The number of words starting from I are $= 5! = 120$
The number of words starting from KA are $= 4! = 24$
The number of words starting from KI are $= 4! = 24$
The number of words starting from KN are $= 4! = 24$
The number of words starting from KRA are $= 3! = 6$
The number of words starting from KRIA are $= 2! = 2$
The number of words starting from KRIN are $= 2! = 2$
The number of words starting from KRISA are $= 1! = 1$
The number of words starting from KRISNA are $= 1! = 1$
So, the final rank of the word KRISHNA is $= 2\left( {120} \right) + 3\left( {24} \right) + 6 + 2\left( 2 \right) + 2\left( 1 \right) = 324$
Hence, the rank of the word KRISHNA is 324.

So, the correct answer is “Option A”.

Note: In order to solve such type students must use the basic method and should alphabetically count the number of each word from different combinations. Students must not solve the problem by simple counting and should rather use the method of permutation and combination.