SOLUTION: Six points are placed on a circle. What is the greatest number of different lines that can be drawn so that each line passes through two of these points? (A) 12 (B) 15 (C) 25

Question 265915: Six points are placed on a circle. What is the greatest number of different lines that can be drawn so that each line passes through two of these points?
(A) 12 (B) 15 (C) 25 (D) 30 (E) 36
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
Six points are placed on a circle. What is the greatest number of different lines that can be drawn so that each line passes through two of these points?
(A) 12 (B) 15 (C) 25 (D) 30 (E) 36
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If the points are A,B,C,D,E, and F then you can choose the beginning point as any of the 6 letters and the ending point any of the remaining 5 letters, That's 6 times 5 or 30 ways to indicate a line. However, the line, say AB, is also counted as BA among the 30, since if the beginning letter and the ending letter are reversed it's still the same line. So 30 is twice too many, so we take half of 30 and get 15. So the answer is choice (B).
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Another way to look at it is "6 letters choose 2" or 6C2 = 15
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Edwin

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