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The number of ways to arrange the letters of the word ‘GARDEN’ with vowels in alphabetical order is
- a)360
- b)240
- c)120
- d)480
Correct answer is option 'A'. Can you explain this answer?
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The number of ways to arrange the letters of the word ‘GARDEN&rs...
Understanding the Problem
To find the number of ways to arrange the letters of the word "GARDEN" with vowels in alphabetical order, we first identify the vowels and consonants in the word.
Vowels and Consonants
- Vowels: A, E
- Consonants: G, R, D, N
Step 1: Total Letters and Arrangements
The word "GARDEN" has 6 letters. If there were no restrictions, the total arrangements of these letters would be calculated as follows:
- Total arrangements = 6! = 720
Step 2: Arranging Vowels in Order
Since the vowels A and E must be in alphabetical order, we consider the arrangements where A comes before E.
Step 3: Fixing Vowels' Order
For every arrangement of the 6 letters, A and E can be placed in any of the 2 positions, but since they must be in alphabetical order, we only need to consider one arrangement (A before E).
Step 4: Choosing Positions for Vowels
We choose 2 out of the 6 positions for the vowels (A and E). The number of ways to choose 2 positions from 6 is given by:
- Number of ways to choose positions = C(6, 2) = 15
Step 5: Arranging Consonants
The remaining 4 positions will be filled by the consonants G, R, D, N. These can be arranged in:
- Arrangements of consonants = 4! = 24
Final Calculation
Now, we multiply the number of ways to choose the positions for the vowels by the arrangements of the consonants:
- Total arrangements with vowels in order = C(6, 2) * 4! = 15 * 24 = 360
Thus, the correct answer is option 'A' - 360.
To find the number of ways to arrange the letters of the word "GARDEN" with vowels in alphabetical order, we first identify the vowels and consonants in the word.
Vowels and Consonants
- Vowels: A, E
- Consonants: G, R, D, N
Step 1: Total Letters and Arrangements
The word "GARDEN" has 6 letters. If there were no restrictions, the total arrangements of these letters would be calculated as follows:
- Total arrangements = 6! = 720
Step 2: Arranging Vowels in Order
Since the vowels A and E must be in alphabetical order, we consider the arrangements where A comes before E.
Step 3: Fixing Vowels' Order
For every arrangement of the 6 letters, A and E can be placed in any of the 2 positions, but since they must be in alphabetical order, we only need to consider one arrangement (A before E).
Step 4: Choosing Positions for Vowels
We choose 2 out of the 6 positions for the vowels (A and E). The number of ways to choose 2 positions from 6 is given by:
- Number of ways to choose positions = C(6, 2) = 15
Step 5: Arranging Consonants
The remaining 4 positions will be filled by the consonants G, R, D, N. These can be arranged in:
- Arrangements of consonants = 4! = 24
Final Calculation
Now, we multiply the number of ways to choose the positions for the vowels by the arrangements of the consonants:
- Total arrangements with vowels in order = C(6, 2) * 4! = 15 * 24 = 360
Thus, the correct answer is option 'A' - 360.
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Community Answer
The number of ways to arrange the letters of the word ‘GARDEN&rs...
6P6-2 = 6P4
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The number of ways to arrange the letters of the word ‘GARDEN’ with vowels in alphabetical order isa)360b)240c)120d)480Correct answer is option 'A'. Can you explain this answer?
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The number of ways to arrange the letters of the word ‘GARDEN’ with vowels in alphabetical order isa)360b)240c)120d)480Correct answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The number of ways to arrange the letters of the word ‘GARDEN’ with vowels in alphabetical order isa)360b)240c)120d)480Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of ways to arrange the letters of the word ‘GARDEN’ with vowels in alphabetical order isa)360b)240c)120d)480Correct answer is option 'A'. Can you explain this answer?.
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