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In how many different ways can the letters of the word ‘DETAIL’ be arranged in such a way that the vowels occupy only the odd positions?
- a)32
- b)48
- c)36
- d)60
- e)120
Correct answer is option 'C'. Can you explain this answer?
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In how many different ways can the letters of the word ‘DETAIL&r...
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"DIFFERENT" be arranged?
The word "DIFFERENT" has a total of 9 letters.
Since there are repeated letters in the word, we need to consider the number of ways to arrange the letters taking into account the repeated letters.
The repeated letters are "E" (3 times) and "N" (2 times).
Thus, the number of ways to arrange the letters of the word "DIFFERENT" can be calculated using the formula for permutations of objects with identical items:
Number of ways = Total number of arrangements / (Number of arrangements for repeated items)
Total number of arrangements = 9!
Number of arrangements for repeated items = 3! * 2!
Therefore, the number of different ways to arrange the letters of the word "DIFFERENT" is:
Number of ways = 9! / (3! * 2!)
Calculating this expression:
Number of ways = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (3 * 2 * 1 * 2 * 1)
Number of ways = 362,880 / 12
Number of ways = 30,240
Therefore, there are 30,240 different ways to arrange the letters of the word "DIFFERENT".
The word "DIFFERENT" has a total of 9 letters.
Since there are repeated letters in the word, we need to consider the number of ways to arrange the letters taking into account the repeated letters.
The repeated letters are "E" (3 times) and "N" (2 times).
Thus, the number of ways to arrange the letters of the word "DIFFERENT" can be calculated using the formula for permutations of objects with identical items:
Number of ways = Total number of arrangements / (Number of arrangements for repeated items)
Total number of arrangements = 9!
Number of arrangements for repeated items = 3! * 2!
Therefore, the number of different ways to arrange the letters of the word "DIFFERENT" is:
Number of ways = 9! / (3! * 2!)
Calculating this expression:
Number of ways = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (3 * 2 * 1 * 2 * 1)
Number of ways = 362,880 / 12
Number of ways = 30,240
Therefore, there are 30,240 different ways to arrange the letters of the word "DIFFERENT".
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In how many different ways can the letters of the word ‘DETAIL’ be arranged in such a way that the vowels occupy only the odd positions?a)32b)48c)36d)60e)120Correct answer is option 'C'. Can you explain this answer?
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In how many different ways can the letters of the word ‘DETAIL’ be arranged in such a way that the vowels occupy only the odd positions?a)32b)48c)36d)60e)120Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about In how many different ways can the letters of the word ‘DETAIL’ be arranged in such a way that the vowels occupy only the odd positions?a)32b)48c)36d)60e)120Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many different ways can the letters of the word ‘DETAIL’ be arranged in such a way that the vowels occupy only the odd positions?a)32b)48c)36d)60e)120Correct answer is option 'C'. Can you explain this answer?.
In how many different ways can the letters of the word ‘DETAIL’ be arranged in such a way that the vowels occupy only the odd positions?a)32b)48c)36d)60e)120Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about In how many different ways can the letters of the word ‘DETAIL’ be arranged in such a way that the vowels occupy only the odd positions?a)32b)48c)36d)60e)120Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many different ways can the letters of the word ‘DETAIL’ be arranged in such a way that the vowels occupy only the odd positions?a)32b)48c)36d)60e)120Correct answer is option 'C'. Can you explain this answer?.
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