Multiple choice

If two letters are taken at random from the word HOME, what is the probability that none of the letters would be vowels?

  1. $\dfrac{1}{6}$
  2. $\dfrac{1}{3}$
  3. $\dfrac{2}{3}$
  4. $\dfrac{11}{49}$
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A Correct answer
Explanation

Word HOME has 4 letters: H, O, M, E. Vowels are O, E. Consonants are H, M. Total ways to pick 2 letters = 4C2 = 6. Ways to pick 2 consonants = 2C2 = 1. Probability = 1/6.

AI explanation

The word HOME has 4 letters in total, consisting of 2 vowels and 2 consonants. The total number of ways to select 2 letters from 4 is 4C2, which equals 6. The number of ways to select 2 consonants, ensuring no vowels are chosen, is 2C2, which equals 1. The probability is the favorable outcomes divided by the total outcomes, giving 1 divided by 6.

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