Multiple choice

What is the probability that a word formed by randomly arranging the letters of the word "MANGO" starts with a vowel?

  1. 1/3

  2. 3/5

  3. 1/2

  4. 2/5

  5. 1/5
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D Correct answer
Explanation

The word MANGO has 5 letters: M, A, N, G, O. There are 5! = 120 total arrangements. The vowels are A and O. If the word starts with a vowel, the first position can be filled in 2 ways (A or O), and the remaining 4 positions in 4! = 24 ways. Total favorable arrangements = 2 * 24 = 48. Probability = 48 / 120 = 2/5.

AI explanation

Using the fundamental principle of counting, the total number of possible arrangements for the 5 letters in MANGO is 5! = 120. The word contains exactly 2 vowels (A and O), so there are 2 ways to choose the starting letter and 4! = 24 ways to arrange the remaining letters, giving 2 x 24 = 48 favorable arrangements. The probability is therefore 48 / 120, which simplifies to 2/5.

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