Class JEE Mathematics Statistics and Probability Q #991
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4 Marks 2025 JEE Main 2025 (Online) 28th January Evening Shift MCQ SINGLE
Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is:
(A) $\frac{1}{4}$
(B) $\frac{1}{2}$
(C) $\frac{1}{3}$
(D) $\frac{2}{3}$
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Correct Answer: B
Explanation
A, E,G R D N

Probabllity $(P) = \frac{\text{favourable case}}{\text{Total case}}$

(when A & E are in order)

Total case = $6!$

Favourable case = ${6}C_2 . 4! = (15)4! = (30)4!$

$P = \frac{(15)4!}{(30)4!} = \frac{1}{2}$

Probability when not in order = $1 - \frac{1}{2} = \frac{1}{2}$

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