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
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
The correct option is A 324
When arranged alphabetically, the letters of the word KRISNA are A, L, 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 arrangments of the remaining 4 letters = 4!
The number of words starting with KI = Number of arrangements of the remaining 3 letters.
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.
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
324
When arranged alphabetically, the letters of the word KRISNA are A, L, 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 arrangments of the remaining 4 letters = 4!
The number of words starting with KI = Number of arrangements of the remaining 3 letters.
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.
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
