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?
Answer & explanation
Answer: (b) 16
In the worst case you pick all 8 green and all 7 white balls first — 15 balls and still no red. The next ball must be red, so 16 balls guarantee at least one of each colour.
- Worst case: the two largest colour groups come out first — 8 green + 7 white = 15 balls.
- Only red balls remain, so the 16th ball is red.
- 16 is enough in every case, and 15 is not (the all-green-and-white case), so the minimum is 16.
Remember · To be assured of one of each colour, take every ball except the smallest colour group, then add 1.
Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·