there are 6 points on a plane. out of these 6 points, if 3 are collinear, then how many triangle can be formed using the given 6 points?

22

Step-by-step explanation:

I drew this many times.

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Like that. IGNORE THE DASHES.

Then, starting with the middle point on the left, I went through all triangles that use that point. That totals to 12, which I got by looking at each total of the triangles formed using that point and one other point. 4 triangles can be formed using the left 2 points and a third point. 3 more can be formed from the mid-left point, the top right point, and a third point that doesn’t include the already-used top left point. 1 more can be formed using the mid-left point and the mid-right point (the third point in this case is the bottom point). Finally, 1 more comes from the mid-left point, the middle point, and the bottom point. That makes 12 for the triangles that use the mid-left point. I repeated this with the mid-right point, making sure not to use the mid-left point ever again. That gave me 6 more triangles. I repeated again, with the top left point (no longer using the middle left or middle right points), and got 3 more. That’s 12+6+3 so far, or 21. Lastly, there is only one triangle that can be formed using the top right point that doesn’t also use the middle left, top left, or middle right points. That would be top right, middle, and bottom. That makes 22.