Multiple choice

The letters of the word EQUATION are arranged in such a way that all vowels as well as consonants are together. How many such arrangements are there?

  1. 240

  2. 720

  3. 1440

  4. 1620
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The word EQUATION has 8 distinct letters: 5 vowels (E, U, A, I, O) and 3 consonants (Q, T, N). Treating vowels as one block and consonants as another, we have 2! ways to arrange the blocks, 5! ways to arrange vowels within their block, and 3! ways to arrange consonants within their block. The total is 2 * 120 * 6 = 1440.

AI explanation

The word EQUATION has 5 vowels and 3 consonants. Treating all vowels as one single unit and all consonants as another gives 2 items that can be arranged in 2! ways. The 5 vowels can be arranged within their unit in 5! ways, and the 3 consonants can be arranged within their unit in 3! ways. The total number of arrangements is 2! multiplied by 5! multiplied by 3!, which equals 2 multiplied by 120 multiplied by 6, yielding 1440.

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