Question

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

• A. $120$
• B. $240$
• C. $360$
• D. $480$

Answer 1

The correct option is C

$360$

Find the arrangement:

Number of ways $n!=n\times (n-1).....3\times 2\times 1$

Given the words, GARDEN

Total number of letters = $6!$

Total number of ways in which all $6$ letters can be arranged $=6!$ ways

Total number of ways in which two vowels (A, E) can be arranged between them $=2!$ ways

Therefore total number of arrangement $=\frac{6!}{2!}=360$

Hence arrangement can be done in $360$ ways and correct option is $\mathbf{\left(}\mathit{C}\mathbf{\right)}\mathbf{.}$.