Multiple choice

A bag contains 5 blue and 4 black balls. Three balls are drawn at random. What is the probability that 2 are blue and 1 is black?

  1. $\dfrac {1}{3}$
  2. $\dfrac {2}{5}$
  3. $\dfrac {1}{6}$

  4. none
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D Correct answer
AI explanation

Using the combinations formula, the total number of ways to draw 3 balls from the 9 available is 9C3, which equals 84. The number of favorable ways to choose 2 blue balls from 5 and 1 black ball from 4 is the product of 5C2 and 4C1, yielding 10 multiplied by 4, which is 40. The probability of this event is the ratio of 40 to 84, which simplifies to 10/21. Since 10/21 is not listed among the first three options, the correct choice is none. The result is none.

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