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lets A1,A2,A3 be three points on a straight line

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lets A1,A2,A3 be three points on a straight line. Lets B1,B2,B3,B4,B5 be five points on a straight line parallel to first one.  Each of the three points on the first line is joined by a straight line to each of the five points on the second line. Further,no three or more of these joining lines met at a point except possibly at the A's or B's. Then the number of point of intersection of the joining lines lying between the two given  straight line
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