SOLUTION: Determine the number of different triangles that can be drawn given eight noncollinear points?

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Question 1181576: Determine the number of different triangles that can be drawn given eight
noncollinear points?
Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
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Each triangle is determined in a UNIQUE way by its three vertices.


THEREFORE, the number of triangle in this problem is equal to the number of all sets of three points 
that can be chosen from 8 given noncollinear points.


It is the number of combinations of 3 points chosen from 8 points


    C%5B8%5D%5E3 = %288%2A7%2A6%29%2F%281%2A2%2A3%29 = 8*7 = 56.    ANSWER

Solved, answered and explained.

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This problem is on COMBINATIONS.


On Combinations,  see introductory lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - OVERVIEW of lessons on Permutations and Combinations
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic  "Combinatorics: Combinations and permutations".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.