The total number of triangles that can be made are 120.
We have a circle and 10 points are placed on it.
We have to find how many possible triangles can be made such that their vertices will be the given points.
What is a Combination?
A combination can be defined as the number of possible arrangements of elements without taking into consideration the order of selection. The number of possible combinations can be given by -
[tex]\frac{n!}{(n-r)!r!}[/tex]
In the question given to us - we have 10 points on circle. Only three points are needed to make a triangle. The order does not matter here, therefore -
[tex]\frac{10!}{(10-3)!3!}\\\\\frac{10!}{7!\times3!} \\\\\frac{10\times9\times8\times7!}{7!\times3\times2\times1}[/tex]
10 x 3 x 4 = 120
Hence, the total number of triangles that can be made are 120.
To solve more questions on combinations, visit the link below -
https://brainly.com/question/13387529
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