### Home > A2C > Chapter 10 > Lesson 10.2.3 > Problem 10-96

Given seven points in a plane, no three of which are collinear:

a. How many different lines are determined by these points?

'No three are colinear' means that any line drawn through two of the points will not intersect any of the other 5 points.

In order for a line to be determined by these points, it must pass through at least two of them.

Write a statement in the form of

C_{n}to describe the situation._{r}How many distinct triangles can be formed?

Write a statement to describe choosing 3 out of the 7 points.

_{7}C_{3}= 35How many distinct quadrilaterals can be formed?

Write a statement to describe choosing

out of the points. Explain why the answers to parts (b) and (c) are the same.

Write the answers to parts (b) and (c) in

C_{n}form, and then in factorial form._{r}

Instead of simplifying, look at the similarities between the expressions.