Fifteen points are evenly spaced on the circumference of a circle. How many combinations of three points can we pick from these 15 that do not form an equilateral triangle?
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Total points = 15
Total ways of choosing 3 points = 15C3 = (15×14×13) / (3×2×1) = 455
An equilateral triangle will form when we choose the:
1 - (1st, 6th, 11th) point
2- (2nd, 7th, 12th) point
3- (3rd, 8th, 13th) poinT
4 - (4th,9tg,14th) point
5- (5th,10th,15th) point
Next triangle (6th,11th,1st) has already come..
So total 5 equilateral triangles
Hence combinations of three points we can pick from these 15 that do not form an equilateral triangle = 455 - 5 = 450
Total ways of choosing 3 points = 15C3 = (15×14×13) / (3×2×1) = 455
An equilateral triangle will form when we choose the:
1 - (1st, 6th, 11th) point
2- (2nd, 7th, 12th) point
3- (3rd, 8th, 13th) poinT
4 - (4th,9tg,14th) point
5- (5th,10th,15th) point
Next triangle (6th,11th,1st) has already come..
So total 5 equilateral triangles
Hence combinations of three points we can pick from these 15 that do not form an equilateral triangle = 455 - 5 = 450
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