Multiple choice

A bag contains $9$ marbles, $3$ of which are red, $3$ of which are blue, and $3$ of which are yellow. If three marbles are selected from the bag at random, what is probability that they are all of different colors?

  1. $\dfrac {1}{15}$
  2. $\dfrac {9}{28}$
  3. $\dfrac {1}{19}$
  4. $\dfrac {1}{20}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total ways to choose 3 marbles from 9 is 9C3 = 84. Favorable ways to choose one of each color (1 red, 1 blue, 1 yellow) is 3C1 * 3C1 * 3C1 = 3 * 3 * 3 = 27. Probability = 27/84 = 9/28.

AI explanation

The total number of ways to select 3 marbles from 9 is calculated using the combinations formula as 9C3 = 84. The number of ways to pick one marble of each color is 3C1 multiplied by 3C1 multiplied by 3C1, which equals 27. The required probability is 27 divided by 84, which simplifies to 9/28.

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