JEE Mains · Maths · STD 11 - 6. permutation and combination
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
- A \(24\)
- B \(56\)
- C \(16\)
- D \(48\)
Answer & Solution
Correct Answer
(C) \(16\)
Step-by-step Solution
Detailed explanation
\(\because\) no. of triangles having no side common with a \(\mathrm{n}\) sided polygon \(=\frac{{ }^n C_1 \cdot{ }^{n-4} C_2}{3}\) \(=\frac{{ }^8 \mathrm{C}_1 \cdot{ }^4 \mathrm{C}_2}{3}=16\)
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