The letters of the word EQUATION are arranged in such a way that all vowels as well as consonants are together. How many such arrangements are there?

• Correct answer
  A

  $240$
• B

  $720$
• C

  $1440$
• D

  $1620$

Solution

Here, word, 'EQUATION' contains 5 vowels (A, E, I, $\mathrm{O}, \mathrm{U})$ and 3 consonants ( $\mathrm{Q}, \mathrm{T}, \mathrm{N}$ ). Two cases are possible here Case (I):
$\begin{aligned} & \text { Number of ways for this arrangement }=(3!) \cdot(5!) \\ & \text {Case(II): }\end{aligned}$
$\begin{aligned} & \text { Number of ways for this arrangement }=(3!) \cdot(5!) \\ & \text {Total required number of ways }=(3!)(5!)+(3!)(5!) \\ & =1440\end{aligned}$

Hence, the correct answer is option: 'A'.