Free Practice Question
PS · Problem Solving
705-805
Combinations
Let AB, CD, EF, GH, and JK be the five diameters of a circle with center O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K and O so as to form a triangle?
Answer Choices
Correct answer marked belowA
165
160
Correct
C
185
D
200
E
225
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Explanation
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Official Explanation
Official
We have 11 points total: A, B, C, D, E, F, G, H, J, K, and O.
Total ways to choose any 3 points out of 11: .
We must subtract the cases where the three chosen points are collinear and do not form a triangle. The only collinear sets occur when the three points lie on the same diameter.…
Total ways to choose any 3 points out of 11: .
We must subtract the cases where the three chosen points are collinear and do not form a triangle. The only collinear sets occur when the three points lie on the same diameter.…
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What it tests
Whether you can count arrangements and selections correctly — permutations vs. combinations.
Common trap
Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.
Details
Difficulty
705-805
Type
PS
Category