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AP EAMCET · Maths · Permutation Combination

The number of ways of arranging all the letters of the word PERFECTION such that there must be exactly two consonants between any two vowels is

  1. A \(4!+6!\)
  2. B \(3!+6!\)
  3. C \(2!3!6!\)
  4. D \(\frac{6!}{4!}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(2!3!6!\)

Step-by-step Solution

Detailed explanation

Vowels: E, E, I, O (4 letters, E repeats 2 times) Consonants: P, R, F, C, T, N (6 distinct letters) Arrangement pattern (V=Vowel, C=Consonant): VCCVCCVCCV Ways to arrange vowels: \( \frac{4!}{2!} \) Ways to arrange consonants: \( 6! \) Total ways:…