There are 9 cups placed on a table arranged in equal number of rows and columns out of which 6 cups contain coffee and 3 cups contain tea. In how many ways can they be arranged so that each row should contain at least one cup of coffee?
Answer & explanation
Answer: (d) 81
The 9 cups form a 3 × 3 grid. Choosing the 3 places for tea can be done in C(9, 3) = 84 ways; only the 3 choices that fill a whole row with tea leave a row without coffee. So 84 − 3 = 81.
- Equal rows and columns with 9 cups means a 3 × 3 grid.
- Cups of the same drink are alike, so an arrangement is fixed by the 3 places holding tea: C(9, 3) = 84.
- A row lacks coffee only when all 3 tea cups fill that row: 3 such arrangements.
- Arrangements with coffee in every row = 84 − 3 = 81.
Remember · ‘At least one’ counts are easiest as total minus the bad cases.
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). ·