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JEE Main 2025 Jan 28 Shift 2, Mathematics Q6: Introduction To Probability

JEE Main2025Jan 28, Shift 2Mathematics
Q.

Let be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set , one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is :

  1. A

  2. B

  3. C

  4. D

Solution

The word GARDEN has 6 distinct letters with two vowels (A, E). Total arrangements .

The two vowels can appear in alphabetical order (A before E) or reverse, and by symmetry exactly half of all arrangements satisfy each ordering. So .

Therefore .

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