Creating Triangles: How Many Can You Make?

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SUMMARY

The discussion focuses on calculating the number of triangles that can be formed using a grid of dots, specifically with seven dots in a horizontal row and four dots in a vertical column. Three distinct methods for forming triangles are outlined: placing one dot at the corner, two dots on the row, and one on the column; two dots on the row and one on the column; and one dot on the row and two on the column. The total number of triangles calculated using combinations is 154, derived from the formulas 7C1 x 4C1, 7C2 x 4C1, and 7C1 x 4C2, resulting in 28, 84, and 42 triangles respectively.

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How many triangles can be made given the following dots?

Triangle.jpg


Thanks a lot!
 
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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?
 
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
 
MichaelLiu said:
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)
 

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