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The letters of the word ‘ZENITH’ are permuted in all possible ways and the words thus formed are arranged as in a dictionary. The rank of the word ‘ZENITH’ is
- a)616
- b)618
- c)597
- d)5930
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The letters of the word ‘ZENITH’ are permuted in all possi...
Rank is 5(5!) + 0.4! + 2(3!) + 1 x 2! + 1 x 1! + 1 = 616
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The letters of the word ‘ZENITH’ are permuted in all possi...
Rank of the word 'ZENITH'
The word 'ZENITH' has 6 letters, with 'E' appearing twice. To find the rank of the word 'ZENITH' when arranged in dictionary order, we need to consider all possible permutations of the letters.
Calculating the rank
1. Arrange the letters of 'ZENITH' in alphabetical order: E, H, I, N, T, Z.
2. Now, consider the word 'ZENITH' and find the number of words that come before it in alphabetical order.
3. For the first letter 'Z', there are 5 letters before it in alphabetical order.
4. For the second letter 'E', there is 1 letter before it in alphabetical order ('H').
5. For the third letter 'N', there are 3 letters before it in alphabetical order ('T', 'Z', 'E').
6. For the fourth letter 'I', there is 1 letter before it in alphabetical order ('N').
7. For the fifth letter 'T', there is 1 letter before it in alphabetical order ('Z').
8. Finally, the last letter 'H' has no letters before it in alphabetical order.
9. Now, calculate the rank using the formula: Rank = (Position of 1st letter * (5!)) + (Position of 2nd letter * (4!)) + (Position of 3rd letter * (3!)) + (Position of 4th letter * (2!)) + (Position of 5th letter * (1!)) + (Position of 6th letter * (0!))
10. Substitute the positions of the letters into the formula and calculate the rank.
Therefore, the rank of the word 'ZENITH' in the dictionary order is 616. Hence, the correct answer is option A.
The word 'ZENITH' has 6 letters, with 'E' appearing twice. To find the rank of the word 'ZENITH' when arranged in dictionary order, we need to consider all possible permutations of the letters.
Calculating the rank
1. Arrange the letters of 'ZENITH' in alphabetical order: E, H, I, N, T, Z.
2. Now, consider the word 'ZENITH' and find the number of words that come before it in alphabetical order.
3. For the first letter 'Z', there are 5 letters before it in alphabetical order.
4. For the second letter 'E', there is 1 letter before it in alphabetical order ('H').
5. For the third letter 'N', there are 3 letters before it in alphabetical order ('T', 'Z', 'E').
6. For the fourth letter 'I', there is 1 letter before it in alphabetical order ('N').
7. For the fifth letter 'T', there is 1 letter before it in alphabetical order ('Z').
8. Finally, the last letter 'H' has no letters before it in alphabetical order.
9. Now, calculate the rank using the formula: Rank = (Position of 1st letter * (5!)) + (Position of 2nd letter * (4!)) + (Position of 3rd letter * (3!)) + (Position of 4th letter * (2!)) + (Position of 5th letter * (1!)) + (Position of 6th letter * (0!))
10. Substitute the positions of the letters into the formula and calculate the rank.
Therefore, the rank of the word 'ZENITH' in the dictionary order is 616. Hence, the correct answer is option A.
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The letters of the word ‘ZENITH’ are permuted in all possible ways and the words thus formed are arranged as in a dictionary. The rank of the word ‘ZENITH’ isa)616b)618c)597d)5930Correct answer is option 'A'. Can you explain this answer?
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