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There are 14 points in a plane, out of which 4 are collinear. Find the number of triangles made by these points .

Q: There are 14 points in a plane, out of which 4 are collinear. Find the number of triangles made by these points .

The required number of triangles = nC3 - mC3 Here, n = 14, m = 4 = 14C3 - 4C3 = (14 x 13 x 12 x 11! ) / (3! x 11!) - 4! / (3! x 1!) = (14 x 13 x 12)/6 - 4/1 = 14 x 26 - 4 = 364 - 4 = 360

Correct Answer: 360

Explanation:

The required number of triangles = ⁿC₃ - ^mC₃
Here, n = 14, m = 4
= ¹⁴C₃ - ⁴C₃
= (14 x 13 x 12 x 11! ) / (3! x 11!) - 4! / (3! x 1!)
= (14 x 13 x 12)/6 - 4/1
= 14 x 26 - 4
= 364 - 4
= 360

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