Question

Number of ways in which the letters of the word ${}^{\prime }GARDE{N}^{\prime }$ can be arranged with vowels in alphabetic order, is

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

Answer 1

Answer: (A)

$360$

The given word $GARDEN$ has $2$ vowels $A$ $\xi$ $E.$

Given that they have to be in the order $AE$ i.e possible words will be

$AE.....,$ $A...E....,$ $A.......E,$ $....A...E$ and so on .

Since there are $2$ letters that must follow a particular order the permutations is given by $\frac{6!}{2!}$ (There are $6$ letters )

$\Rightarrow$ Required $=\frac{720}{2}=360.$

Hence, the answer is $360.$