Question

Namstey !

Question from iit jee mains -2004

from permutations and combinations
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How many ways are there to arrange the letters in the word garden with vowels in alphabetical order
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Answer 1

Hello mate!!

Here's ur answer


So the vowels in "GARDEN" are 'A' and 'E'. Total permutations of the word GARDEN are 6!=720.6!=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 1/21/2. Hence in half of the words, vowels are in alphabetical order. Hence, answer is 720/2=360720/2=360.




Hope it helpful

Answer 2

$\bold \blue{hello \: friends}$

$\bold\green{solution}$

Total number of arrangments of letters in the word GARDEN = 6 ! = 720 there are two words vowel A and E , in half of the arrangments A proceed E and other half A follows E

so , vowels in alphabetical order in

1/2* 720 = 360 Answer ✔

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$\boxed{hope \: it \: helps \: you}$

$\pink{ \star \: muskraj \star}$