Multiple choice

The number of arrangements that can be formed by taking all the letters of the word EQUATION so that no two consonants come together is

  1. 14,400

  2. 13,600

  3. 16,200

  4. 12,500
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The word EQUATION has 8 letters: 5 vowels (E, U, A, I, O) and 3 consonants (Q, T, N). To ensure no two consonants are together, place the 5 vowels first (5! = 120 ways) and then place the 3 consonants in the 6 available gaps (6P3 = 6 * 5 * 4 = 120 ways). Total = 120 * 120 = 14,400.

AI explanation

The word EQUATION has 5 vowels and 3 consonants. Arranging the 5 vowels first gives 5! ways, which equals 120 ways. This creates 6 gaps where the 3 consonants can be placed to remain separate, giving 6P3 ways, which equals 120 ways. Multiplying 120 by 120 yields 14400.

Keep practicing — related questions