Multiple choice

The number of ways in which the letters of the word $COMBINE$ can be arranged so that the words begin and end with a vowel, is

  1. $30$
  2. $504$
  3. $360$
  4. $720$
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A Correct answer
AI explanation

The word COMBINE has 7 letters with 3 vowels (O, I, E) and 4 consonants. Using the permutations formula, select and arrange 2 vowels at the beginning and end in 3P2 = 6 ways. Arrange the remaining 5 letters in the middle in 5! = 120 ways. The total number of arrangements is 6 * 120 = 720. The result is 720.

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