Verified Solution • 2025–26 Session moderate

QJEEM25Ma77ba: JEE Main 2025 Mathematics - Class 12 JEEM25Ma77ba Solution: Let S be the set of all the words that can be formed by…

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:

Multiple Choice Options

  • A 14\frac{1}{4}
  • B 12\frac{1}{2}
  • C 13\frac{1}{3}
  • D 23\frac{2}{3}

Step-by-Step Verified Solution

A, E,G R D N

 Probabllity (P)= favourable case  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!

Probablity when not in order =1−12=12=1-\frac{1}{2}=\frac{1}{2}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring