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JEE Main 202528 JanuaryEvening Shift
Exam
JEE Main
Year
2025
Date
28 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2025 · 28 January · Evening Shift · Mathematics · Probability

Let S be the set of all the words that can be formed by arranging...

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 :

Options

  1. A12\frac{1}{2}
  2. B14\frac{1}{4}
  3. C23\frac{2}{3}
  4. D13\frac{1}{3}

Correct answer

A. 12\frac{1}{2}

Step-by-step solution

A, E,G R D N  Probabllity (P)= favourable case  Total case \text{ Probabllity }(\mathrm{P})=\frac{\text{ favourable case }}{\text{ Total case }} (when A & E are in order) Total case =6=6 ! Favourable case =6C2.4={ }^6 \mathrm{C}_2 .4 ! P=(15)4!(30)4!P=\frac{(15) 4!}{(30) 4!} Probablity when not in order =1−12=12=1-\frac{1}{2}=\frac{1}{2}
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