QUESTION

CSAT

Easy

Maths

Prelims 2023

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

Select an option to attempt

Explanation

Let 12 consecutive things in the circle be x1,X2,X3,X12x_1, X_2, X_3, \dots X_{12}.

We need to select 10 consecutive things out of these 12 things in the circle taken in the clockwise direction.

This selection can be made as follows:

(x1 to x10),(x2 to x11),(x3 to x12),(X4 to x1),(x5 to x2),(x6 to x3),(x7 to x4),(x8 to x5),(x9 to x6),(x10 to X7),(X11 to X8),(X12 to X9)(x_1 \text{ to } x_{10}), (x_2 \text{ to } x_{11}), (x_3 \text{ to } x_{12}), (X_4 \text{ to } x_1), (x_5 \text{ to } x_2), (x_6 \text{ to } x_3), (x_7 \text{ to } x_4), (x_8 \text{ to } x_5), (x_9 \text{ to } x_6), (x_{10} \text{ to } X_7), (X_{11} \text{ to } X_8), (X_{12} \text{ to } X_9)

So, there are 12 possible ways to do so.

Hence, option (C) is correct.

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