Q42 / 90 · JEE Main 2024 (06 Apr Shift 1) · Mathematics

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
    48
  • B
    56
  • C
    24
  • Correct answer
    D
    16

Solution

$\because$ no. of triangles having no side common with a $\mathrm{n}$ $\begin{aligned} & \text { sided polygon }=\frac{{ }^n C_1 \cdot{ }^{n-4} C_2}{3} \\ & =\frac{{ }^8 C_1 \cdot{ }^4 C_2}{3}=16 \end{aligned}$

Hence, the correct answer is option: 'D'.

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