What is the number of selections of 10 consecutive things out of 12 things in a circle taken in the clockwise direction ?
- (a) 3
- (b) 11
- (c) 12 ✓ UPSC's answer
- (d) 66
Why the answer is (c)
• In a circle of 12 things, a block of 10 consecutive things taken clockwise is fixed completely by its starting point.
• Any of the 12 things can be the starting point, and each start gives a different block (because 10 is less than 12).
• For example, starting at 1 gives 1 to 10, starting at 2 gives 2 to 11, and so on round the circle.
• Hence 12 selections, option (c).
Why the other options are wrong
- (a) 3
- Each of the 12 things can start a block, so there are 12 selections, not 3.
- (b) 11
- All 12 starting points give different blocks, not 11.
- (d) 66
- 66 counts unrestricted choices of 2 things to leave out (12C2); the blocks here must be consecutive.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2023, held on 28 May 2023. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.