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JEE Main 20246 AprilMorning Shift

Exam: JEE Main
Year: 2024
Date: 6 April
Shift: Morning Shift
Subject: Mathematics
Chapter: Permutation and Combination

JEE Main 2024 · 6 April · Morning Shift · Mathematics · Permutation and Combination

The number of triangles whose vertices are at the vertices of a...

The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is

Options

A48
B56
C24
D16

Correct answer

D. 16

Step-by-step solution

\because

no. of triangles having no side common with a

\mathrm{n}

\begin{aligned} & \text{ sided polygon }=\frac{{ }^n C_1 \cdot{ }^{n-4} C_2}{3} \\ & =\frac{{ }^8 C_1 \cdot{ }^4 C_2}{3}=16 \end{aligned}

$$

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