Question Detail
Question
How many ways are there to arrange the letters of the word 'GARDEN' with the vowels in alphabetical order?
Correct Answer
Option B is the correct answer.
Detailed Explanation
The word 'GARDEN' has 6 distinct letters: G, A, R, D, E, N.The vowels in 'GARDEN' are A and E.If the vowels must be in alphabetical order, this means 'A' must always come before 'E'.Consider all possible arrangements of the 6 letters, which is 6! = 720.In any arrangement of these 6 letters, for any chosen positions for A and E, there are 2! = 2 ways to arrange A and E (AE or EA).Since only one of these arrangements (AE) is desired, we divide the total number of permutations by 2!.Number of ways = 6! / 2! = 720 / 2 = 360.
Hint
Calculate the total permutations of all letters. For letters that must be in a specific relative order, divide by the factorial of the number of such letters.