Question 1120837
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You have  {{{6*((4*3)/2)}}} = 6*6 = 36 different triangles having one vertex in line "a" and two vertices in line "b".


Plus you have {{{4*((6*5)/2)}}} = 4*15 = 60 other triangles, having one vertex in the line "b" and 2 vertices in the line "a".


In all, there are 36 + 60 = 96 triangles.
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Solved.