Triangles are formed by joining vertices of a octagon then number of triangle

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In which atmost one side common with the side of polygon is 48

Total number of triangle 56

In which exactly one side common with the side of octagon is 32

At least one side common with the side polygon 50

answer is A, B, D.

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Detailed Solution

Total number of triangle $= {}^{8}C_{3} = 56$
Number of triangle having exactly one side common with the polygon $= 8 \times 4 = 32$
Number of triangle having exactly two side common with the polygon = 8
Number of triangle having no side common with the polygon = 16

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