Multiple choice

In a bag three are infinitely many red ,white and black balls which are identical. If ten balls are selected at random then the probability that selection includes atleast one ball from each colour is

  1. $\dfrac{5}{{11}}$
  2. $\dfrac{6}{{11}}$
  3. $\dfrac{7}{{11}}$
  4. $\dfrac{4}{{11}}$
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B Correct answer
AI explanation

Selecting 10 balls from 3 identical colors where balls of each color are infinite is a stars and bars problem, giving a total of 12C2 = 66 total ways. The probability of getting at least one ball of each color is 1 minus the probability of missing at least one color. The number of ways to choose all 10 balls from only 2 colors is 3 x 11C2 = 165, and the number of ways to choose all 10 balls from a single color is 3, so the probability of the complement is (165 - 3)/666 = 5/11, making the target probability 1 - 5/11 = 6/11.

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