Number of triangle that can be made using the vertices of a polygon of 10 sides as their vertices and having exactly one side common with the polygon is

Question

Match the following

	Column 1		Column - 2
A)	Number of triangle that can be made using the vertices of a polygon of 10 sides as their vertices and having exactly one side common with the polygon is	p)	75
B)	Number of triangle that can be made using the vertices of a polygon of 10 sides as their vertices and having exactly 2 sides common with the polygon is	q)	110
C)	Number of quadrilaterals that can be made using the vertices of a polygon of 10 sides as their vertices and having exactly 2 sides common with the polygon is	r)	60
D)	Number of quadrilaterals that can be made using the vertices of a polygon of 10 sides as their vertices and having 3 sides common with the polygon is	s)	10

Smart Achievers · Accepted Answer

(3)

(A) No. of such triangles = $10 \times {}^{6}C_{1} = 60$

(B) No. of such triangles = 10

(C) No. of such quadrilaterals $= 10 \times 5 + \frac{10 \times 5}{2}$ $= 50 + 25$ $= 75$

(D) No. of such quadrilaterals = 10 (when four consecutive points are taken)

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