Mathematics · Probability

JEE Main 2025 — 28 January, Evening Shift — Question 6

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 :

Option A:
$\frac{1}{4}$
Option B:
$\frac{2}{3}$
Option C:
$\frac{1}{3}$
Option D:
$\frac{1}{2}$
Correct

Answer: D

Step-by-step solution

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 $={ }^{6} \mathrm{C}_{2} .4$ !

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

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

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 28 January, Evening Shift
Subject: Mathematics
Chapter: Probability
Topic: Problems based on P & C

Bag B 1 contains 6 white and 4 blue balls, Bag B 2 contains 4 white and 6 blue balls, and Bag B 3 contains 5 white and 5 blue balls. One of…

Answer: D

Step-by-step solution

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