Multiple choice

How many words can be formed with the letters of the word PATLIPUTRA without changing the relative positions of vowels and consonants?

  1. 2160

  2. 3250

  3. 3230

  4. 3660
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

PATLIPUTRA has 10 letters: P, A, T, L, I, P, U, T, R, A. Vowels are A, I, U, A (4). Consonants are P, T, L, P, T, R (6). Vowels are at positions 2, 4, 7, 10. Consonants are at 1, 3, 5, 6, 8, 9. Arrange 4 vowels (A, A, I, U) in 4!/2! = 12 ways. Arrange 6 consonants (P, P, T, T, L, R) in 6!/(2!*2!) = 720/4 = 180 ways. Total = 12 * 180 = 2160.

AI explanation

In the word PATLIPUTRA, there are 4 vowels (A, A, I, U) and 6 consonants (P, T, L, P, T, R) that must stay in their original positions. The 4 vowel positions can be filled in 4! divided by 2! ways, which is 12, and the 6 consonant positions can be filled in 6! divided by (2! multiplied by 2!) ways because P and T each repeat twice, which is 180. Multiplying 180 by 12 gives 2160 total ways.

Keep practicing — related questions