Browse Questions

How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?

$\begin{array}{1 1}(A)\;120\\(B)\;240\\(C)\;360\\(D)\;480\end{array}$

Toolbox:
• $n!=n(n-1)(n-2)(n-3).....(3)(2)(1)$
Total number of ways in which all letters of the word GARDEN can be arranged =6!
There are two vowels in the word GARDEN
Total number of ways in which these two vowels can be arranged =2!
$\therefore$ Total number of required ways =$\large\frac{6!}{2!}$
$\Rightarrow \large\frac{6\times 5\times 4\times 3\times 2!}{2!}$
$\Rightarrow 360$
Hence (C) is the correct answer.