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Question
If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is
Options
324
341
359
none of these
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Solution
324
When arranged alphabetically, the letters of the word KRISNA are A, I, K, N, R and S.
Number of words that will be formed with A as the first letter = Number of arrangements of the remaining 5 letters = 5!
Number of words that will be formed with I as the first letter = Number of arrangements of the remaining 5 letters = 5!
∴ The number of words beginning with KA = Number of arrangements of the remaining 4 letters = 4!
The number of words starting with KI = Number of arrangements of the remaining 4 letters = 4!
Alphabetically, the next letter will be KR.
Number of words starting with KR followed by A, i.e. KRA = Number of arrangements of the remaining 3 letters = 3!
Number of words starting with KRI followed by A, i.e. KRIA = Number of arrangements of the remaining 2 letters = 2!
Number of words starting with KRI followed by N, i.e. KRIN = Number of arrangements of the remaining 2 letters = 2!
The first word beginning with KRIS is the word KRISAN and the next word is KRISNA.
∴ Rank of the word KRISNA = 5! + 5! + 4! + 4! + 4! + 3! + 2! + 2! + 2 = 324
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