Q23 of 31 Page 7

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

In ORDINATE,


The vowels are O,I,A,E.



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


Now 1st place can be filled in 4 ways.


3rd will be in 3 ways.


5th will be in 2 ways.


7th 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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