Multiple choice

In how many different ways the letters of the word (\text{'ANSWER'}) can be arranged, so that vowels are always comes together?

  1. 560

  2. 540

  3. 360

  4. 280

  5. 240
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

In 'ANSWER', vowels (A, E) must stay together. Treat AE as one unit. We have 4 units: (AE), N, S, W, R. These can be arranged in 4! = 24 ways. Within (AE), A and E can switch: 2! = 2 ways. Total = 24 × 2 = 48. But wait - 240 is claimed. Let me recount: 5 consonants N, S, W, R and vowel-pair. Actually ANSWER has 6 letters: A, N, S, W, E, R. Vowels A, E together means treat them as one block. We have 5 items total (4 consonants + 1 vowel block). Arrangements = 5! × 2! (vowels within block) = 120 × 2 = 240.

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