# How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical  order? Option 1) 360 Option 2) 240 Option 3) 120 Option 4) 480

As we learnt in

The Number of ways of Arrangement of objects -

The number of ways of n different objects taken all at a time $=\ ^{n}p_{n}=n!$

- wherein

Where 0! = 1

Total are arrangements of the word GARDEN are 6!

Half of them have A and E in alphabetical order.

Thus ways are $\frac{6!}{2}=360$

Correct option is 1.

Option 1)

360

This is the correct option.

Option 2)

240

This is an incorrect option.

Option 3)

120

This is an incorrect option.

Option 4)

480

This is an incorrect option.

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