SOLUTION: If 7 points are found on a circle, how many triangles can be drawn using any 3 of these points as vertices? Multiple choice answers: a. 210 b. 38 c. 35 d. 44

Question 1162103: If 7 points are found on a circle, how many triangles can be drawn using any 3 of these points as vertices?
Multiple choice answers:
a. 210
b. 38
c. 35
d. 44
Answer by ikleyn(52798) (Show Source): You can put this solution on YOUR website!
.


Every triple of the points determines one unique triangle;  and vice versa, each triangle determines one triple of the points.

The order of points inside each triple does not matter.



    Notice that in the circle, NO ONE TRIPLE of points lies on a straight line (!).

    It is where in the solution, the circle is used as a locus of the points (!)



Therefore, the number of triangles is the number of combinations of 7 points taken 3 at a time


     =  = 7*5 = 35.     ANSWER

Solved.

-----------------

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.

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