What is the number of numbers of the form 0·XY, where X and Y are distinct non-zero digits?
Answer & explanation
Answer: (a) 72
X can be any of the 9 non-zero digits and Y any of the other 8, giving 9 × 8 = 72 different decimals.
- X can be any of 1–9: 9 choices.
- Y must be non-zero and different from X: 8 choices.
- Total = 9 × 8 = 72, and each ordered pair gives a different number.
Remember · Distinct choices from the same pool: n × (n − 1) ordered pairs.
Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·