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There are 12 points on a semicircle as shown :Number of triangles that can be made using these points.

Question

There are 12 points on a semicircle as shown :Number of triangles that can be made using these points.

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Solution

To find the number of triangles that can be made using these points, we need to use the combination formula. The combination formula is nCr = n! / r!(n-r)!, where n is the total number of items, r is the number of items to choose, and "!" denotes factorial.

Step 1: Identify the total number of points. In this case, n = 12.

Step 2: Identify the number of points to choose to form a triangle. In this case, r = 3.

Step 3: Substitute n and r into the combination formula.

So, 12C3 = 12! / 3!(12-3)! = 220.

Therefore, 220 triangles can be made using these 12 points on a semicircle.

This problem has been solved

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