Mathematics · Permutations and Combinations

JEE Main 2024 — 6 April, Shift 1 — Question 16

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

Option A:
24
Option B:
56
Option C:
16
Correct
Option D:
48

Answer: C

Step-by-step solution

$\because$ no. of triangles having no side common with an

sided polygon $=\frac{{ }^{\mathrm{n}} \mathrm{C}_{1} \cdot{ }^{\mathrm{n}-4} \mathrm{C}_{2}}{3}$ $=\frac{{ }^{8} \mathrm{C}_{1} \cdot{ }^{4} \mathrm{C}_{2}}{3}=16$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 6 April, Shift 1
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Applications of Permuations and Combination