What is the number of selections of 10 consecutive things out of 12 things in a circle taken in the clockwise direction?

1. A. 3
2. B. 11
3. C. 12
4. D. 66

Answer: C

Explanation

Consider the 12 things arranged in a circle, labeled 1 to 12 in a clockwise direction. We need to select 10 consecutive things. This means we are essentially choosing a starting point for our sequence of 10. If we start at thing 1, the selection is (1, 2, 3, 4, 5, 6, 7, 8, 9, 10). If we start at thing 2, the selection is (2, 3, 4, 5, 6, 7, 8, 9, 10, 11). This continues until we start at thing 12, which gives the selection (12, 1, 2, 3, 4, 5, 6, 7, 8, 9). Each of the 12 things can serve as the unique starting point for a sequence of 10 consecutive things. Therefore, there are 12 such selections.