Minimalist IAS
CSAT 2022 paper

UPSC CSE CSAT 2022 · Question 79 · Counting, permutations & probability

What is the number of numbers of the form 0·XY, where X and Y are distinct non-zero digits?

CSAT 2022 · Q79

Counting, permutations & probability Easy

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.

  1. X can be any of 1–9: 9 choices.
  2. Y must be non-zero and different from X: 8 choices.
  3. 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). ·

More on Counting, permutations & probability

All Counting, permutations & probability questions →