How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?
- A
- B
- C
- D
Solution & Step-by-step Explanation
The word GARDEN has distinct letters.
Total number of ways to arrange the letters is
The vowels in the word are A and E.
In any random arrangement of these letters, there are only two possibilities for the relative order of A and E:A appears before E.E appears before A.
Since the letters are distinct and the positions are symmetric, in exactly half of the total arrangements, A will be before E, and in the other half, E will be before A.
The alphabetical order for vowels A and E is (A, E).
Thus, the number of arrangements where vowels are in alphabetical order is:
.
Total number of ways to arrange the letters is
The vowels in the word are A and E.
In any random arrangement of these letters, there are only two possibilities for the relative order of A and E:A appears before E.E appears before A.
Since the letters are distinct and the positions are symmetric, in exactly half of the total arrangements, A will be before E, and in the other half, E will be before A.
The alphabetical order for vowels A and E is (A, E).
Thus, the number of arrangements where vowels are in alphabetical order is:
.