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The number of different words that can be formed from the letters of the word INTERMEDIATE.Such that two vowels never come together is ________

$\begin{array}{1 1}(A)\;151200\\(B)\;150200\\(C)\;153200\\(D)\;154200\end{array} $

2 Answers

  • $C(n,r)=\large\frac{n!}{r!(n-r)!}$
Total no of consonants =6
Total no of vowels =6
Total no of letters in the word INTERMEDIATE =12
No of ways of arranging the consonants of which two are alike =$\large\frac{6!}{2!}$
$\Rightarrow \large\frac{6\times 5\times 4\times 3\times 2}{2}$
$\Rightarrow 360$
No of ways of arranging the vowels =$7P_6\times \large\frac{1}{3!}\times \frac{1}{2!}$
$\Rightarrow \large\frac{7!}{1!}\times \frac{1}{3!}\times \frac{1}{2!}$
$\Rightarrow \large\frac{7\times 6\times 5\times 4\times 3!}{3!\times 2}$
$\Rightarrow 420$
Total no of ways =$420\times 360$
$\Rightarrow 151200$
Hence (A) is the correct answer.
answered May 16, 2014 by sreemathi.v

Find the number of permutations of the letters of the word “INTERMEDIATE” such that the vowels always occupy odd places.

answered Jan 28 by nikitadalwale95

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