Question

Three noncollinear points determine a triangle. How many triangles can be formed with 8 points, no three of which are collinear?
A. 56

B. 24

C. 336

D. 6720

Answer 1

n C r = (n!)/(r!(n-r)!)


8 C 3 = (8!)/(3!(8-3)!)


8 C 3 = (8!)/(3!5!)


8 C 3 = (8*7*6*5!)/(3!5!)


8 C 3 = (8*7*6)/(3!)


8 C 3 = (8*7*6)/(3*2*1)


8 C 3 = (8*7*2)/(2*1)


8 C 3 = (8*7)/(1)


8 C 3 = 56


So there are 56 different triangles.