A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is the minimum number of balls that must be picked up from the bag (without replacing any of it) so that at least one ball from each color is drawn? 

A bag contains 20 balls Calculation: ⇒ We have to at least one ball of each colour ⇒ Even if we pick 8 balls there is a probability all of them may be green. Hence we must pick more than 8 balls for sure ⇒ Now even we pick (8 + 7) balls or 15 balls, there is a  probability that all of them may be green and white only with no red ball picked at all. ⇒ Hence taking the worst possible scenario in consideration we must pick = 15 + 1 = 16 ∴ The required result will be 16.