Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XI  >>  Math  >>  Permutations and Combinations
0 votes

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} $

Can you answer this question?

1 Answer

0 votes
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

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App