Question

How many words are formed if the letters of the word garden?

Answer 1

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.