Permutations And Combinations


How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?

  • 120

  • 480

  • 360

  • 240




A total number of ways in which all letters can be arranged in alphabetical order = 6! There are two vowels in the word GARDEN. A total number of ways in which these two vowels can be arranged = 2!
∴ Total number of required ways 
∴ Total number of required waysspace equals space fraction numerator 6 factorial over denominator 2 factorial end fraction space equals space 360

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