INTERMEDIATE : Not talking about Level. Part-IV

I N T E R M E D I A T E \huge INTERMEDIATE How many words can be made using all of the letters of the word I N T E R M E D I A T E INTERMEDIATE if all of the vowels appear in one string?


The answer is 151200.

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2 solutions

Bk Lim
Apr 5, 2015

Ways to arrange all vowels = 6 ! 2 ! 3 ! = 60 \frac{6!}{2!3!}=60 Ways to arrange all consonants = 6 ! 2 ! = 360 \frac{6!}{2!}=360

Since all consonants must be placed together, we have 7 ways to do that, i.e starting from 1st, 2nd,...7th place.

Words can be made = 60 × 360 × 7 = 151200 60\times360\times7=151200

keeping 6 consonants together(let call them <C>),we have 7 letters(6 are vowels).They can b arranged in 7!/(3!2!) ways...the 6 consonants can be arranged in 6!/2! ways...hence total no. of comb= (7!/(3!2!))X(6!/2!) =151200

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