Question

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

Answer 1

Answer:

Hence in half of the words, vowels are in alphabetical order. Hence, answer is 720/2=360

Answer 2

Answer:

So the vowels in "GARDEN" are 'A' and 'E'. Total permutations of the word GARDEN are 6! = 720 In half of them, A will occur before E and in the other half of the permutaions, E will occur before A. This is obvious as "A before E" and "E before A" are equally likely and exclusive(nothing other than these two can happen) events.

So both must have probability 1/2. Hence in half of the words, vowels are in alphabetical order. Hence, answer is 720/2 = 360