Question

The number of ways in which the letter of the word 'VERTICAL' can be arranged without changing the order of the vowels is

• A. 6!×3!
• B. $\frac{8!}{3}$
• C. 6!×3
• D. $\frac{8!}{3!}$

Answer 1

Answer: (D)

$\frac{8!}{3!}$

Answer 2

Given :
Word is VERTICAL.
In this word, 3 three vowels are there i.e E, I, A.
Number of ways that out of 8 alphabets
3 vowels (EIA) can be chosen are 8C3
and remaining 5 letters can be arranged in 5 ! ways.
Therefore, the number of ways :
$={^8C_3}\times5!=\frac{8!}{3!}$
So, the correct option is (D) : $\frac{8!}{3!}$