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
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
Updated On: Feb 22, 2024
- 324
- 341
- 359
- None of these
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The Correct Option is A
Solution and Explanation
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
Hence, rank of word �KRISNA
= 2(120) + 3(24) + 6 + 2(2) + 2(1) = 324
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
Hence, rank of word �KRISNA
= 2(120) + 3(24) + 6 + 2(2) + 2(1) = 324
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Concepts Used:
Permutations
A permutation is an arrangement of multiple objects in a particular order taken a few or all at a time. The formula for permutation is as follows:
\(^nP_r = \frac{n!}{(n-r)!}\)
nPr = permutation
n = total number of objects
r = number of objects selected
Types of Permutation
- Permutation of n different things where repeating is not allowed
- Permutation of n different things where repeating is allowed
- Permutation of similar kinds or duplicate objects