how many 5 letter word containing 3 vowels and 2 consonants can be formed using the letters of word ' EQUATION' so that the two consonant occur together ?
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The word EQUATION contains 5 vowels and 3 consonants.
Number of ways of choosing 3 vowels from 5 is C(5, 3).
Number of ways of choosing 2 consonants from 3 is C(3, 2).
Number of ways of selecting 5 vowels and 3 consonants is C(5, 3)×C(3, 2)
Number of different words formed by these 5 letters is 5!
So the answer is C(5, 3)×C(3, 2)×5!
= 10×3×120
= 3600 words
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