Multiple choice

In how many ways can we arrange the letters of the word ORANGE so that all the vowels come together always?

  1. 200

  2. 180

  3. 160

  4. 144
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D Correct answer
AI explanation

The word ORANGE has 3 vowels and 3 consonants. Treating the 3 vowels as a single block gives 4 entities to arrange in 4 factorial ways. The 3 vowels within their block can be arranged in 3 factorial ways. Multiplying these gives 4 factorial times 3 factorial, which is 24 times 6, resulting in 144.

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