### Home > CCA2 > Chapter Ch10 > Lesson 10.2.2 > Problem 10-118

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

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

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

to describe the situation. How many distinct triangles can be formed?

Write a statement to describe choosing

out of the points. _{ }How 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

_{ }form, and then in factorial form.

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