Multiple choice

The number of words, that can be formed by using all letters of the word DAUGHTER, if relative order of vowels and consonants remains same, are

  1. $2880$
  2. $6720$
  3. $720$
  4. $3600$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

DAUGHTER has 8 letters: 3 vowels (A, U, E) and 5 consonants (D, G, H, T, R). The relative order of vowels and consonants must remain the same. There are 3! ways to arrange vowels and 5! ways to arrange consonants. Total ways = 3! * 5! = 6 * 120 = 720.

AI explanation

The word DAUGHTER has 8 distinct letters with 3 vowels (A, U, E) and 5 consonants. Since their relative positions must remain unchanged, the 3 vowels can only be arranged among themselves in 3! ways, and the 5 consonants can be arranged among themselves in 5! ways. Multiplying these possibilities gives 3! * 5! = 6 * 120 = 720.

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