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In how many ways can we sort the letters of the word MANAGEMENT so that the comparative position of vowels and consonants remains the same as in MANAGEMENT.
- a)1280
- b)720
- c)960
- d)1080
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
In how many ways can we sort the letters of the word MANAGEMENT so tha...
Given:
Word = MANAGEMENT
Calculation:
Vowel occupy 4 places then !4
∵ A and E are repeated then !4/(!2 × !2)
Consonant occupy 6 places then !6
⇒ M and N are repeated then !6/(!2 × !2)
= 6 × 180 = 1080
Word = MANAGEMENT
Calculation:
Vowel occupy 4 places then !4
∵ A and E are repeated then !4/(!2 × !2)
Consonant occupy 6 places then !6
⇒ M and N are repeated then !6/(!2 × !2)
= 6 × 180 = 1080
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Community Answer
In how many ways can we sort the letters of the word MANAGEMENT so tha...
Approach:
To solve this problem, we need to consider the relative positions of vowels and consonants in the word MANAGEMENT. We cannot change the order of vowels and consonants while sorting the letters.
Calculation:
- The word MANAGEMENT has 4 vowels (A, A, E, E) and 5 consonants (M, N, G, M, N, T).
- The number of ways to arrange the vowels among themselves = 4!/2! = 12 (dividing by 2! for repeated vowels)
- The number of ways to arrange the consonants among themselves = 5!/2! = 60 (dividing by 2! for repeated consonants)
- The total number of ways to arrange the letters while maintaining the relative positions of vowels and consonants = 12 * 60 = 720 * 3 = 2160
Correct Answer:
The correct answer is option D) 1080.
To solve this problem, we need to consider the relative positions of vowels and consonants in the word MANAGEMENT. We cannot change the order of vowels and consonants while sorting the letters.
Calculation:
- The word MANAGEMENT has 4 vowels (A, A, E, E) and 5 consonants (M, N, G, M, N, T).
- The number of ways to arrange the vowels among themselves = 4!/2! = 12 (dividing by 2! for repeated vowels)
- The number of ways to arrange the consonants among themselves = 5!/2! = 60 (dividing by 2! for repeated consonants)
- The total number of ways to arrange the letters while maintaining the relative positions of vowels and consonants = 12 * 60 = 720 * 3 = 2160
Correct Answer:
The correct answer is option D) 1080.
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In how many ways can we sort the letters of the word MANAGEMENT so that the comparative position of vowels and consonants remains the same as in MANAGEMENT.a)1280b)720c)960d)1080Correct answer is option 'D'. Can you explain this answer?
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In how many ways can we sort the letters of the word MANAGEMENT so that the comparative position of vowels and consonants remains the same as in MANAGEMENT.a)1280b)720c)960d)1080Correct answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about In how many ways can we sort the letters of the word MANAGEMENT so that the comparative position of vowels and consonants remains the same as in MANAGEMENT.a)1280b)720c)960d)1080Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many ways can we sort the letters of the word MANAGEMENT so that the comparative position of vowels and consonants remains the same as in MANAGEMENT.a)1280b)720c)960d)1080Correct answer is option 'D'. Can you explain this answer?.
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