Question

Number of words that can be formed with letters of the word ALGBRA so that all the vowels are separated (or no two vowels come together) is

• A. 720
• B. 2160
• C. 1440
• D. None of these

Answer 1

Answer: (A)

720

Answer 2

Vowels are A, E, A. Consonants are L, G, B, R x L x G x B x R x

Since there is no restriction on consonants, we must place them first and they can be arranged in 4! = 24 ways.

Now, to arrange vowels so that no two of them are together we have 5 places, shown by ‘X’ above.

Out of these 5 places 3 can be selected in $5C_{3}$ ways and then one arrangement can be made in $\frac{3!}{2!}$ ways.

∴ Required ways = 4! $5C_{3}$. $\frac{3!}{2!}$ = 720.