5. Two parallel lines are given. On one of them, six different points are chosen, and on the other, five different points. How many triangles are there whose vertices are located at the chosen points on the lines?

Each task is scored out of 10 points.

The use of a pocket calculator or any reference materials is not allowed.
5. A triangle is obtained if the endpoints of any line segment on one line are connected to any point on another line.

On the first line, there are six points, and they determine $6 \cdot 5: 2=15$ line segments.

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Each of these line segments can be connected to each of the five points on the second line. The number of triangles whose one side is on the first line and the third vertex is on the second line is $15 \cdot 5=75$.

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On the second line, there are five points, and they determine $5 \cdot 4: 2=10$ line segments.

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If we connect these with the six points on the first line, we get $10 \cdot 6=60$ triangles whose one side is on the second line and the third vertex is on the first line.

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The total number of triangles is $75+60=135$.

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TOTAL 10 POINTS