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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2024 · Mathematics · Permutation and Combination

The letters of the word EQUATION are arranged in such a way that...

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?

Options

  1. A240240
  2. B720720
  3. C14401440
  4. D16201620

Correct answer

A. 240240

Step-by-step solution

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