### Home > CCA2 > Chapter 10 > Lesson 10.2.2 > Problem10-118

10-118.

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

1. 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 $_nC_r$ to describe the situation.

2. How many distinct triangles can be formed?

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

$_7C_3=35$

3. How many distinct quadrilaterals can be formed?

Write a statement to describe choosing $4$ out of the $7$ points.

4. Explain why the answers to parts (b) and (c) are the same.

Write the answers to parts (b) and (c) in $_nC_r$ form, and then in factorial form.
Instead of simplifying, look at the similarities between the expressions.