What is the number of selections of 10 consecutive things out of 12 things in a circle taken in the clockwise direction?
Answer & explanation
Answer: (c) 12
Going clockwise, a block of 10 consecutive things is fixed by its starting point, and each of the 12 things can be the start. So there are 12 selections.
- Taken clockwise, a run of 10 consecutive things is decided by where it starts.
- Each of the 12 things can be the starting point, and different starts give different sets.
- Number of selections = 12.
- Check: each selection leaves out 2 neighbouring things, and a circle of 12 has exactly 12 neighbouring pairs.
Remember · In a circle of n items, the number of blocks of k consecutive items (k < n) is n.
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). ·