Multiple choice

In how many ways can the letters of word EDUCATION be arranged such that NO two Consonants (C,D,T,N) appear together?

  1. 5!*4!*3!

  2. 15*5!*4!*2!

  3. 15*5!*4!

  4. 15*15!*4!
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

EDUCATION has 9 letters: 5 vowels (E, U, A, I, O) and 4 consonants (D, C, T, N). Arrange vowels in 5! ways. There are 6 gaps created by vowels. Choose 4 gaps for consonants in 6C4 = 15 ways. Arrange consonants in 4! ways. Total = 5! * 15 * 4!.

AI explanation

The word EDUCATION has 5 vowels (E, U, A, I, O) and 4 consonants (D, C, T, N), and no letters repeat. To ensure no two consonants are together, we first arrange the 5 vowels in 5! ways, creating 6 gaps (including the ends) for the consonants. We then choose 4 of these 6 gaps to place the 4 consonants, which can be done in 6C4 ways, and arrange the consonants in those spots in 4! ways. The total ways are 5! times 6C4 times 4!, which simplifies to 15 times 5! times 4!. The result is 15*5!*4!.

Keep practicing — related questions