Multiple choice

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. $64$
  2. $45$
  3. $46$

  4. none of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

AI explanation

The box contains a total of 9 balls (2 white, 3 black, and 4 red). The total number of ways to draw any 3 balls from 9 is 9C3, which equals 84. To find the draws with at least one black ball, we subtract the number of draws with no black balls (choosing 3 from the 6 non-black balls) from the total. So, 9C3 - 6C3 equals 84 - 20, giving 64 ways.

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