Ten distinct points are identified on the circumference of a circle. How many different convex quadrilaterals can be formed if each vertex must be one of these 10 points?

Guest Apr 21, 2020

#2**+1 **

trianlges 10C3 = 120

quadrialterals 10C4 = 210

pentagons 10C5 = 252

hexagons 10C6 = 210

heptagons 10C7 = 120

octogons 10C8 = 45

nonogons 10C9 = 10

deacagons 10C10 = 1

120+210+252+210+120+45+10+1 = 968 cyclic polygons

But then the question only wants the quadrilaterals so I get **210**

Melody Apr 22, 2020