Multiple choice

The number of words that can be formed, with the letters of the work $PATALIPUTRA$ without changing the relative order of the vowels and consonants is

  1. $3600$
  2. $4200$
  3. $3680$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

There are 5 vowels, with A repeated 3 times, giving 5!/3! arrangements. The 6 consonants have P and T repeated twice each, giving 6!/(2!2!) arrangements, and their product is 3600.

AI explanation

The word PATALIPUTRA has 11 letters with 6 consonants (P, T, L, P, T, R) and 5 vowels (A, A, I, U, A). The consonants can be arranged among themselves in 6! / (2! 2!) = 180 ways. The vowels can be arranged among themselves in 5! / 3! = 20 ways. The total number of words maintaining the relative positions is 180 * 20 = 3600. The correct result is 3600.

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