Multiple choice

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colour is

  1. $\displaystyle \frac{2}{7}$
  2. $\displaystyle \frac{1}{21}$
  3. $\displaystyle \frac{2}{23}$
  4. $\displaystyle \frac{1}{3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total balls = 9. Ways to pick 3 different colors = (3 red * 4 blue * 2 green) = 24. Total ways to pick 3 balls = 9C3 = (9*8*7)/(3*2*1) = 84. Probability = 24/84 = 2/7.

AI explanation

The total number of ways to draw 3 balls from 9 is 9C3, which equals 84. To get one ball of each color, we multiply the combinations 3C1, 4C1, and 2C1, which gives 24. The probability is 24/84, which simplifies to 2/7.

Keep practicing — related questions