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Question

How many ways are there to arrange the letters of the word EDUCATION so that all the following three conditions hold?

– the vowels occur in the same order (EUAIO);

– the consonants occur in the same order(DCTN);

– no two consonants are next to each other.


A

15

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B

24

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C

72

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D

120

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Solution

The correct option is A

15


Vowels can be arranged in one way.

There will be 6 gaps around them. We need 4 gaps as the arrangement can be done in one way.

Therefore, 6C4=15


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