Multiple choice

Three balls are drawn at random from an urn containing 5 yellow,4 white, 3 blue balls.What is the probability that the three balls are of different colours?

  1. 17/30

  2. 3/44

  3. 3/11

  4. 3/22
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total balls = 5+4+3 = 12. Selecting 3 balls: total ways = 12C3 = (12*11*10)/(3*2*1) = 220. Ways to pick one of each color = 5C1 * 4C1 * 3C1 = 5 * 4 * 3 = 60. Probability = 60/220 = 3/11.

AI explanation

Using the fundamental principle of counting, the total number of ways to draw three balls from twelve is the combination (12 choose 3), which equals 220. The number of ways to draw one ball of each color is the product 5 times 4 times 3, which equals 60. By the definition of probability, the chance is the favorable outcomes divided by total outcomes, so 60 divided by 220 simplifies to 3/11.

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