Multiple choice

A box contains $2$ white balls and $4$ red balls, in how many ways can three balls be drawn from the box, if at least one red ball is to be included in the draw?

  1. $32$
  2. $48$
  3. $20$
  4. $96$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total ways to draw 3 balls from 6 (2 white, 4 red) is 6C3 = 20. Ways to draw 3 balls with no red (all white) is 2C3 = 0. Since there are only 2 white balls, it is impossible to draw 3 white balls. Thus, all combinations of 3 balls must contain at least one red ball. Total ways = 20.

AI explanation

The box contains a total of 6 balls, so the total ways to draw any 3 balls is 6C3, which equals 20. The number of ways to draw 3 balls with no red balls, meaning all 3 are drawn from the 2 white balls, is 2C3, which equals 0. Using the complementary counting method, subtract the invalid draws from the total draws to get 20 minus 0, resulting in 20 ways.

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