Question 199702This question is from textbook algebra 2 with trigonmetry
: question:How many lines are determined by 8 points, no 3 of which are collinear? how many triangles are determined by the same points if no 4 are coplanar.
This question is from textbook algebra 2 with trigonmetry
Answer by tutorvolunteer(9)   (Show Source):
You can put this solution on YOUR website! The first part of the question uses combinations. Since running a line through points A and B makes no difference from running a line through points B and A, we know this is a combination problem (not a permutation problem) since order does not matter.
Therefore, 2 Choose 8 is the number of lines determined by 8 points, since a line consists of only 2 points.
The second part of the question uses the same concept, only now, 3 points are involved (consisting of the triangle's vertices.) 3 Choose 8.
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