Multiple choice

In how many ways the letter of the word "ORANGE" be arranged so that vowels are not separated?

  1. $120$
  2. $144$
  3. $720$
  4. $600$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Treat the vowels (O, A, E) as a single block. There are 4 items to arrange: {OAE}, R, N, G. These can be arranged in 4! = 24 ways. Within the block, the 3 vowels can be arranged in 3! = 6 ways. Total arrangements = 24 * 6 = 144.

AI explanation

The word ORANGE has three vowels (O, A, E) and three consonants, allowing us to treat the vowels as a single block. This single block along with the three consonants gives 4 items to arrange, which can be done in 4 factorial, or 24, ways. The three vowels within their block can be arranged among themselves in 3 factorial, or 6, ways. The total number of arrangements is 24 multiplied by 6, which equals 144.

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