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In how many ways can the letters of the word PERMUTATIONS be arranged if the Vowels are together?

$\begin{array}{1 1}(A)\;1814400\\(B)\;2419200\\(C)\;2419220\\(D)\;2419240\end{array} $

1 Answer

There are 12 letters in the word PERMUTATIONS which have T two times
Now the vowels $a,e,i,o,u$ are together.Let it be considered in one block
The letters of vowels can be arranged in $5!$ ways
Thus there are 7 letters and 1 block of vowels with T two times
$\therefore$ Number of arrangements =$\large\frac{8!}{2!}$$\times 5!$
$\Rightarrow \large\frac{8!5!}{2}$
$\Rightarrow 2419200$
Hence (B) is the correct answer.
answered May 13, 2014 by sreemathi.v

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