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  • Fill in the Blanks The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.

Fill in the Blanks  The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.

[Hint: Number of ways of arranging 6 consonants of which two are alike is \frac{6!}{2!} and number of ways of arranging vowels  =^7P_6\times \frac{1}{3!}\times \frac{1}{2!}

Answers (1)

. Vowels in INTERMEDIATE are I, E, E, I, A, E and consonants N, T, R, M, D, T   

First six consonants are arranged in \frac{6!}{2!}ways.

 In the 7 gaps, six vowels are arranged in ^7C_6*\frac{6!}{2!3!}  ways 

 Total number of words \frac{6!}{2!}*^7C_6*\frac{6!}{2!3!}=360*7*60=151200

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