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
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Permutations
-> 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
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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(52797) (Show Source):
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
