Multiple choice

An urn contains $3$ red, $4$ blue and $2$ green balls. Three balls are selected. Find the probability that they are of different colors.

  1. $\dfrac{1}{2}$
  2. $\dfrac{2}{23}$
  3. $\dfrac{2}{7}$
  4. $\dfrac{1}{3}$
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A Correct answer
AI explanation

The total number of ways to select three balls from the nine balls is the combination of 9 taken 3 at a time, which is 84. To get one ball of each color, we multiply the individual selections: the combination of 3 taken 1 for red, the combination of 4 taken 1 for blue, and the combination of 2 taken 1 for green, giving 3 times 4 times 2 equals 24. Dividing the favorable outcomes by the total outcomes gives a probability of 24 divided by 84, which simplifies to 1/2.

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