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JEE Previous Year Question

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

Topic: JEE PYQ

Answer: D. Full step-by-step solution below.

A $48$
B $56$
C $24$
D $16$

Correct answer: D

Solution

(d) no. of triangles having no side common with a n sided polygon = \frac{^{n} C _{1} \cdot ^{n - 4} C _{2}}{3} = \frac{^{8} C _{1} \cdot ^{4} C _{2}}{3} = 16

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