How many1. Straight line 2. Triangles can be formed by joining 12 poi

1.	How many1. Straight line 2. Triangles can be formed by joining 12 points, 4 of which are collinear.
Answer» 1. Number of straight lines that can be formed using 12 points = 12C₂ = \(\frac{12 \times 11}{1 \times 2}\) = 66. Number of straight lines that can be formed using 4 collinear points = 4C₂ = \(\frac{4 \times 3}{1 \times 2}\) = 6. Since the 4 points are collinear, the required number of lines = 66 – 6 + 1 = 61. 2. Number of triangles that can be formed using 12 points = 12C₃ =\( \frac{12 \times 11 \times 10}{1 \times 2 \times 3}\) = 220. Number of triangles that can be formed using 4 collinear points = 4C₃ = 4. Since the 4 points are collinear, the required number of triangles = 220 – 4 = 216.

How many1. Straight line 2. Triangles can be formed by joining 12 points, 4 of which are collinear.

Answer»

1. Number of straight lines that can be formed using 12 points = 12C₂ = \(\frac{12 \times 11}{1 \times 2}\) = 66. Number of straight lines that can be formed using 4 collinear points = 4C₂ = \(\frac{4 \times 3}{1 \times 2}\) = 6.

Since the 4 points are collinear, the required number of lines = 66 – 6 + 1 = 61.

2. Number of triangles that can be formed using 12 points = 12C₃ =\( \frac{12 \times 11 \times 10}{1 \times 2 \times 3}\) = 220.

Number of triangles that can be formed using 4 collinear points = 4C₃ = 4.

Since the 4 points are collinear, the required number of triangles = 220 – 4 = 216.

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