Selecting consecutive items in a circle
Question
What is the number of selections of 10 consecutive things out of 12 things in a circle taken in the clockwise direction?
Options
3
11
12
66
Explanation
Imagine 12 objects arranged in a circular formation. Selecting a block of 10 consecutive things in a fixed clockwise direction is completely determined by choosing the starting point of that block.
Since there are exactly 12 distinct objects that can serve as the initial item for the clockwise group, there are exactly 12 unique blocks of 10 consecutive items. Alternatively, selecting 10 consecutive items in a circle is logically identical to choosing which 2 consecutive items are left behind; there are exactly 12 ways to select 2 adjacent items to drop from a ring of 12.
Answer: (c).
Question details
Year
2023
Paper
CSAT
Question
Q48
Section
Numerical Ability
Sub-topic
Circular Permutations
Type
Number theory
Difficulty
Easy
Source hint
Number theory
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