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?

To be assured of picking at least one ball of each colour, we must consider the worst-case scenario. The worst-case scenario is that we pick all balls of two colours before we are forced to pick a ball of the third colour. 1. Identify the two largest groups of balls: Green (8 balls) and White (7 balls). 2. In the worst case, you would pick all 8 green balls and all 7 white balls first. Total balls picked so far = 8 (green) + 7 (white) = 15 balls. 3. At this point, you have exhausted all green and white balls. The remaining balls in the bag are all red. 4. The very next ball you pick (the 16th ball) must therefore be red. So, 15 (all green and all white) + 1 (the first red ball) = 16 balls. Therefore, picking 16 balls guarantees that you have at least one ball of each colour. Option B is correct because 16 balls ensure that even in the most unlucky scenario, you will have picked all balls of the two most numerous colours, and then one of the remaining colour.