How many triangles can be made by joining 12 points in a plane, given that seven are in one line?

To find how many triangles can be formed by joining 12 points in a plane, where 7 of these points are collinear (i.e., on the same straight line), we need to break the problem into two steps: 

### Step 1: Calculate the total number of triangles from 12 points
In general, to form a triangle, we must choose 3 points from the 12 given points. The formula to choose 3 points from \( n \) points is the combination formula:
\[
C(n, 3) = \frac{n!}{3!(n-3)!}
\]
For \( n = 12 \):
\[
C(

How many triangles can be made by joining 12 points in a plane, given that seven are in one line?

Find out how many triangles can be formed by joining 12 points in a plane when 7 points are collinear. Learn the use of combinatorics and geometry concepts with step-by-step solutions. Ideal for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation