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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
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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