Consider 6 points, two of which are A and B, such that each pair of points is connected by a
line segment and no three points are collinear. Compute the number of distinct paths from A
to B such that no point is visited more than once. Answers:
A) 61  B) 62  C) 63  D) 64  E) 65
We consider cases based on the length of the path. Note that there is 1 path of   length 1, 4 paths of length 2, 4 *3 = 12 paths of length 3, 4* 3 *2 = 12 paths of length 4,   4 * 3 * 2 * 1= 
<gadget id="calculator">4 * 3 * 2 * 1</gadget>
<output>24</output>
24 paths of length 5, and no paths of length 6 or greater. Therefore, there are a   total of 1 + 4 + 12 + 24 + 24= 
<gadget id="calculator">1 + 4 + 12 + 24 + 24</gadget>
<output>65</output>
65 distinct paths.   correct answer 65
<result>E</result>
Consider 6 points, two of which are A and B, such that each pair of points is connected by a
line segment and no three points are collinear. Compute the number of distinct paths from A
to B such that no point is visited more than once.