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)
- (B)
- (C)
- (D)✓ Correct
Answer: (D)
Solution
The word GARDEN has 6 distinct letters, so has arrangements.
In any arrangement, the two vowels A and E occupy two of the six positions; swapping A and E in that arrangement gives another valid word. Exactly one of each such pair has the vowels in alphabetical order (A before E), so exactly half of all 720 words have the vowels in order and half do not.
The probability that the vowels are NOT in alphabetical order is .
In any arrangement, the two vowels A and E occupy two of the six positions; swapping A and E in that arrangement gives another valid word. Exactly one of each such pair has the vowels in alphabetical order (A before E), so exactly half of all 720 words have the vowels in order and half do not.
The probability that the vowels are NOT in alphabetical order is .
JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Single correct option