1. ## combination problem

there are two lines.One lines has 3 points and the other line has 6 points.How many triangles can be constructed by using the points on these two lines?

2. Originally Posted by mastermin346
there are two lines.One lines has 3 points and the other line has 6 points.How many triangles can be constructed by using the points on these two lines?

Dear mastermin346,

We have choose two points from one line and the another point from the other line.

If we choose the two points from the three point line, number of ways this could be done= $^{3}C_{2}\times~^{6}C_{1}=3\times{6}=18$

If we choose the two points from the six point line, number of traingles that could be constructed= $^{6}C_{2}\times~^{3}C_{1}=15\times{3}=45$

Therefore total number of different traingles that could be constructed= $45+18=63$

Hope this helps you.