Raj has ten pairs of red, nine pairs of white and eight pairs of black shoes in a box. If he randomly picks shoes one by one (without replacement) from the box to get a red pair of shoes to wear, what is the maximum number of attempts he has to make?
Answer & explanation
Answer: (d) 45
In the worst case Raj first takes out every white and black shoe, and then every red shoe for one foot. A pair he can wear needs one left and one right shoe, so the pair is certain only on the next draw: 18 + 16 + 10 + 1 = 45.
- The box has 20 red shoes (10 left, 10 right), 18 white shoes and 16 black shoes.
- Worst case: all 18 white and all 16 black shoes come out first: 34 draws and still no red pair.
- Next, all 10 red shoes of one foot (say all left shoes) come out: 44 draws and still no pair to wear.
- The 45th draw has to be a red right shoe, which completes a red pair. Maximum attempts = 34 + 10 + 1 = 45.
- Check: ignoring left and right would give 34 + 2 = 36, the trap option; a wearable pair needs one shoe of each foot.
Remember · Worst-case questions: use up every unhelpful draw first, including same-foot or same-type items, then add one.
Question and answer: UPSC's official GS Paper II (2023, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·