Question

How many words are formed if the letter of the word GARDEN are arranged with the vowels in alphabetical order?

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

Answer 1

The correct option is C $360$

Number of letters in the word GARDEN$=6$

Total number of words formed from GARDEN$=6!$

A and E are the two vowels in the word and it should be in alphabetical order.

Number of ways of arranging the word GARDEN with the vowels in alphabetical order is half the total number of the words formed from GARDEN

The required way of arrangement$=\frac{6!}{2}$

$=\frac{6\times 5\times 4\times 3\times 2\times 1}{2}$

$=6\times 5\times 4\times 3$

$=360$