Multiple choice

A box contains 4 white balls, 5 black balls and 7 green balls. In how many ways can 4 balls be drawn from the box, if at least one white ball, one black ball and one green ball is to be included in a draw?

  1. 910

  2. 920

  3. 890

  4. 940

  5. 840

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total balls = 4 white + 5 black + 7 green = 16. We need 4 balls with at least one of each color. Valid distributions: (1W,1B,2G), (1W,2B,1G), (2W,1B,1G). Calculate: 4C1×5C1×7C2 + 4C1×5C2×7C1 + 4C2×5C1×7C1 = 4×5×21 + 4×10×7 + 6×5×7 = 420 + 280 + 210 = 910.