Multiple choice

In how many ways the letters of the word $'CORPORATION'$ can be arranged so that the relative positions of vowels and consonants is not changed.

  1. $6400$
  2. $4800$
  3. $3600$
  4. $7200$
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D Correct answer
AI explanation

The word CORPORATION has 5 vowels (O, O, A, I, O) and 6 consonants (C, R, P, R, T, N). Using the permutations of identical objects formula, the 5 vowels can be arranged in their 5 relative positions in 5! / 3! = 20 ways. The 6 consonants can be arranged in their 6 relative positions in 6! / 2! = 360 ways. The total number of arrangements is 20 * 360 = 7200. The result is 7200.

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