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

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G Prasad

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As there are only 2 vowels, there will be equal no. of cases with 'a' before 'e' and 'a' after 'e'. So required no. of arrangements = 6!/2 = 360.
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Total number of ways in which we can arrange the word garden is 6! ways. Now we have 2 vowels "a" and "e". In half of the cases "a" is to the left of "e" and in the remaining half of the cases "a" is to the right of "e". So for alphabets to be in ascending order "a" should be placed towards left of "e"....
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Total number of ways in which we can arrange the word garden is 6! ways. Now we have 2 vowels "a" and "e". In half of the cases "a" is to the left of "e" and in the remaining half of the cases "a" is to the right of "e". So for alphabets to be in ascending order "a" should be placed towards left of "e". So total number of ways = 6!/2. read less
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The word GARDEN has 6 letters. so, Total number of ways = 6! A & E are the two vowels in that word GARDEN . so vowels can be arranged = 2! . Therefore the required number of ways = 6! * 2! =360.
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