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 blindfolded (without replacing any of it) to be assured of picking at least one ball of each colour?

Correct Option: 16

To guarantee that we have picked at least one ball of each of the three colours (green, white, and red), we must prepare for the worst-case scenario. The bag contains 8 green, 7 white, and 5 red balls. The worst-case scenario is that we repeatedly draw balls from the two colours with the highest quantities first without getting any of the third colour. The two largest groups of balls are green (8) and white (7). In the absolute worst-case sequence, we could pick all 8 green balls and all 7 white balls consecutively, totaling 8 + 7 = 15 balls, without ever drawing a single red ball. At this stage, only red balls remain in the bag. Therefore, the very next ball we pick (the 16th ball) is guaranteed to be red, completing the requirement of having at least one ball of each colour. Thus, the minimum number of balls to pick is 15 + 1 = 16.