Multiple choice

Directions: The following question has four choices, out of which ONLY ONE is correct. A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box, if at least one black ball is to be included in the draw?

  1. 18

  2. 45

  3. 64

  4. 72

  5. 52
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total balls = 2+3+4 = 9. Total ways to draw 3 balls = 9C3 = 84. Ways to draw 3 balls with no black balls (only white/red) = 6C3 = 20. Ways with at least one black ball = 84 - 20 = 64.

AI explanation

Using the method of combinations, the total ways to draw any three balls from the nine available is 9 choose 3, which equals 84. The number of ways to draw three balls with none being black means choosing all three from the six other balls, which is 6 choose 3, equaling 20. Using the complementary counting principle, the ways to draw at least one black ball is 84 minus 20. The result is 64.

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