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.
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.
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