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How many words can be formed from the letters of the word ‘ORDINATE’ so that vowels occupy odd places?

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How many words can be formed from the letters of the word ‘ORDINATE’ so that vowels occupy odd places?

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VCVCVCVC : vowels can occupy V places and consonants can occupy c places. Possible combinations of arrangements = 4!

 = 24 

Similar 4 consonants (different) and 4 spaces combinations of arrangements = 4! = 24 

Thus, total combinations = 24 × 24 = 576

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