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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2015 · Mathematics · Permutation and Combination

How many words can be formed using all the letters of the word...

How many words can be formed using all the letters of the word ‘NATION’ so that all the three vowels should never come together?

Options

  1. A354
  2. B348
  3. C288
  4. DNone of these

Correct answer

C. 288

Step-by-step solution

The given word is 'NATION'. Total number of words that can be formed from given word 'NATION' =6!2!=6×5×4×3×2!2!=\frac{6!}{2!}=\frac{6 \times 5 \times 4 \times 3 \times 2!}{2!}=360Nownumbersofwordsthatcanbeformedfromgivenword′NATION′,sothatallvowelsnevercometogether.Now numbers of words that can be formed from given word 'NATION', so that all vowels never come together.=360−[4!×3!2!]=360−[24×3]=360−72=288\begin{aligned} & =360-\left[4!\times \frac{3!}{2!}\right] \\ & =360-[24 \times 3] \\ & =360-72=288 \end{aligned}∴\therefore \quad Option (C) is correct.
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