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?
- A.17
- B.16
- C.13
- D.11
▶ Answer & Explanation
Correct answer: B. 16
To guarantee at least one ball of each color, we must consider the worst-case scenario. This involves picking all the balls of the two most numerous colors first. In this case, the two largest groups are green balls (8) and white balls (7). So, in the worst case, one might pick all 8 green balls and all 7 white balls, totaling 15 balls. The very next ball picked, the 16th ball, must then be of the remaining color (red) to ensure representation of all three colors.
Source: UPSC csat 2017