Multiple choice

Three balls are drawn at random from a collection of $7$ white, $12$ green and $4$ red balls. The probability that each is different colour is

  1. $\dfrac{48}{253}$
  2. $\dfrac{64}{253}$
  3. $\dfrac{23}{253}$
  4. $\dfrac{56}{253}$
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A Correct answer
Explanation

Total balls = 7+12+4 = 23. Ways to choose 3 = 23C3 = 1771. Ways to choose 1 of each = 7C1 * 12C1 * 4C1 = 7 * 12 * 4 = 336. Probability = 336 / 1771 = 48 / 253.

AI explanation

The collection has a total of 23 balls. The total number of ways to draw three balls is 23C3, which equals (23 times 22 times 21) divided by 6, or 1771. The number of ways to draw one ball of each color is the product 7C1 times 12C1 times 4C1, which equals 7 times 12 times 4, or 336. The probability is therefore 336 divided by 1771, which simplifies to 48/253.