<p>this is a math question on the free response section
The 6 cabins at a camp are arranged so that there is exactly 1 straight path between each 2 of the cabins, but no 3 of them are on a straight path. What is the total number of such straight paths joining these cabins?</p>
<p>the answer is supposed to be 15 ...but I can't really visualize it because I don't exactly understand what it's asking me to do.
can anyone help explain this problem to me?</p>
<p>what book/source is this Q from?</p>
<p>Try imagining them arranged in a circle. That formation fits that description above.</p>
<p>it's actually from the college board's online course and they give an explanation.... but I don't understand it:</p>
<p>"The correct answer is 15 . For convenience, call the 6 cabins A, B, C, D, E, and F. Name a straight path between two cabins by giving the cabins that it connects; for example, the 5 paths from cabin A to the other cabins are AB, AC, AD, AE, and AF. There are a total of 6 x 5 names for the straight paths between the 6 cabins. However, each path has exactly two different names in this scheme; for example, BD and DB are names for the same path. Therefore, there are just 1/2(30)= 15 paths."
can someone please explain it in different words?</p>
<p>Alright, what they are asking for is to draw lines that connect two cabins together, and keep drawing them until all cabins have been connected. Now if you have 6 cabins, how many lines can you draw starting from one cabin so that it is connected to all the other cabins? 5. Since each cabin is no different from the other cabins, that makes a total of 6x5 = 30 lines drawn. But wait, you will be counting each line twice if you just multiply by 5 (like counting a line from cabin B to cabin A and cabin A to cabin B) so divide by two to account for this and you have 15</p>
<p>Thank you so much. I understand it now , yay!</p>