Multiple choice

In how many ways can the word VALEDICTORY be arranged so that all vowels come together ?

  1. 8!/4!

  2. 8! × 2!

  3. 8! - 4!

  4. 8! × 4!

  5. None of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

VALEDICTORY has 11 letters: V, A, L, E, D, I, C, T, O, R, Y. Vowels are A, E, I, O (4). Consonants are V, L, D, C, T, R, Y (7). Treating vowels as one unit, we have 7 consonants + 1 unit = 8 items. These can be arranged in 8! ways. The 4 vowels can be arranged in 4! ways. Total = 8! * 4!.

AI explanation

The word VALEDICTORY has eight consonants and four vowels (A, E, I, O). To keep the vowels together, treat them as a single block, which can be internally arranged in 4! ways. This block is then arranged along with the eight distinct consonants, giving 9! total arrangements for the blocks. Therefore, the total arrangements are 9! * 4!, which is not listed among the options, making None of the above the correct choice.

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