Question

Number of words that can be formed with letters of the word $ALGEBRA$ 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)

$720$

-L-G-B-R-

Possible ways to arrange consonants among themselves $=41$

Now we need to find the no. of ways we can arrange $3$ vowels in $5$ places. This could be done by ${}^5{C}_3\times \frac{3!}{2!}$

Hence the total no. of ways $=4!\times {}^5{C}_3\times \frac{3!}{2!}$

$=24\times 10\times 3=720$.