Question

Ten points lie on the circumference of a circle. Calculate the value that results when the number of triangles that can be created by connecting these points is subtracted from the number of heptagons(seven-sided polygons) that can be created by connected these points.

• A. $210$
• B. $35$
• C. $21$
• D. $4$
• E. $0$

Answer 1

The correct option is E $0$

Triangle has three vertices, so we have to connect three points out of ten points to form a triangle, so number of ways three points can be selected from ten points is ${{}^{10}C}_3$.
Heptagon has seven vertices, so we have to connect seven points out of ten points to form a heptagon. So number of ways seven points can be selected from ten points is ${{}^{10}C}_7$.
The difference of those two is ${{}^{10}C}_3-{{}^{10}C}_7=120-120=0$.