MHB Creating Triangles: How Many Can You Make?

[MichaelLiu]

How many triangles can be made given the following dots?

Thanks a lot!

 

[Opalg]

Apart from the location at the top left corner of the diagram, there are seven locations on the horizontal row, and four locations on the vertical column. There are three ways to place dots on three of these locations to form a triangle:

First way: one dot at the corner, one from the row of seven, and one from the column of four;
Second way: two dots on the row of seven, and one on the column of four (as in the above diagram);
Third way: one dot on the row of seven, and two on the column of four.

Can you count the number of triangles formed in each of these three ways?

 

[MichaelLiu]

Hey @Opalg ! Thank you for your response!

Would this be the correct answer?

First way:
7C1 x 4C1 = 28

Second way:
7C2 x 4C1 = 84

Third way:
7C1 x 4C2 = 42

28 + 84 + 42 = 154 triangles

 

[Opalg]

Hey @Opalg ! Thank you for your response!

Would this be the correct answer?

First way:
7C1 x 4C1 = 28

Second way:
7C2 x 4C1 = 84

Third way:
7C1 x 4C2 = 42

28 + 84 + 42 = 154 triangles

Looks good to me. (Yes)