Math Problem Statement
How many triangles can be made by joining 12 points in a plane, given that seven are in one line?
Solution
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 points is the combination formula: For : [ C(
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Geometry
Formulas
Combination formula: C(n, 3) = n! / [3!(n-3)!]
Theorems
Triangle Formation Theorem
Suitable Grade Level
Grades 9-12
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