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Q48·CSAT · Prelims 2023

Selecting consecutive items in a circle

NumericalCircular PermutationsNumber theoryEasy

Question

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

Options

a

3

b

11

c

12

Answer
d

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.

For circular arrays, the number of ways to select a continuous block of k consecutive items is always exactly equal to the total number of available items N, independent of k.

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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