A box contains 5 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one white ball is to be included in the draw?

Question: A box contains 5 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one white ball is to be included in the draw?

Solution:
Total number of balls = 5 + 3 + 4
= 12 balls

choosing 3 balls from 12 balls = ¹²C₃
= 220 ways

choosing three balls from black and red balls = ⁷C₃
= 35 ways

∴ ways can 3 balls be drawn from the box, if at least one white ball is to be included in the draw is = 220 - 35 ways
= 185 ways