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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 __ E __ U __ A __ I __ O __ We first fix the vowels in the desired order. This can be done in exactly one way. Now, in the remaining six gaps, four consonants can be filled in 6C4 ways. The desired order of consonants can be achieved in only one way. ∴ Required number of ways =1× 6C4×1=15

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