Answer :

In **ORDINATE,**

The vowels are O,I,A,E.

As vowel can occupy the odd places only, in the above diagram vowels will occupy 1^{st},3^{rd},5^{th},7^{th} places only.

Now 1^{st} place can be filled in 4 ways.

3^{rd} will be in 3 ways.

5^{th} will be in 2 ways.

7^{th} will be in 1 way.

Rest of the words will be filled in even places in 4! Ways.

So total ways = 4× 3× 2× 1× 4!

= 4× 3× 2× 1× 4× 3× 2× 1

= 24× 24

= 576

Hence there are 576 ways.

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