Problem Solving - 7

Eight points lie on the circumfrence of a circle.What is the positive diff b/w th no. of triangles and the no. of quadrilaterals that can be formed by connecting these points?

a. 8

b. 14

c. 56

d. 70

e. 1,344

Answer - B

Since the points are on the circumference of the circle thus no 3 or 4 points will be colinear, thus all points can be used to draw a triangle or quadilateral

Hence 8C4 = 70 and 8C3 = 56 (we make use of combination here because here the order of points do not matter)

Taking the difference we get 70 - 56 = 14.