Multiple choice

In how many different ways can the letters of the word DESIGN be arranged so that the vowels are at the two ends?

  1. 24

  2. 36

  3. 48

  4. 54

  5. 66
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The word DESIGN has 6 letters, consisting of 2 vowels (E, I) and 4 consonants (D, S, G, N). To place the vowels at the two ends, we can arrange them in 2! = 2 ways. The remaining 4 middle positions can be filled by the 4 consonants in 4! = 24 ways, resulting in a total of 2 * 24 = 48 arrangements.

AI explanation

The word DESIGN has 2 vowels (E, I) and 4 consonants (D, S, G, N). The vowels must occupy the two ends, which they can do in 2! ways. The 4 consonants can be arranged in the 4 middle positions in 4! ways, making the total 2! times 4!, which is 2 times 24, or 48.

Keep practicing — related questions