Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Number of words that can be formed with the letters of the word ALGEBRA so that all the vowels are separated (or no two vowels come together)
Text Solution
Verified by ExpertsThe correct answer is:
A
720
Vowels are A, E, A
Consonants are L, G, B, R
XLXGXBXRX
Since there is no restriction on consonants, we must place them first and they can be arranged in 4! = 24 days.
Now to arrange vowels so that no two of them are together we have 5 places (X). Out of these 5 places, 3 can be selected in 5 C 3 ways and then onearrangement can be made in 
ways.
Thus, required ways = 4! x 5 C 3 x 
= 720
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
There are eight rooms on the first floor of a hotel, with four rooms on each side of the corridor, …
From the string abacabababcdced, if 5 letters should be selected, then the number of ways in which …
If the number of ways in which four distinct balls can be put into two identical boxes such that no…
Total number of lines of the form px + qy+ r = 0 (where pq 0) that intersect the ellipse at two i…
The number of words of 4 letters which can be formed with the letters of the word MATHEMATICS is ,…
If 4 dice are rolled once, the number of ways of getting the sum as 10 is K, then the value of is …