Respuesta :

MathPhys

Answer:

18

Step-by-step explanation:

There are 6 dots.  The number of ways we can select 3 from 6 is:

₆C₃ = 6! / (3! (6−3)!)

₆C₃ = 6! / (3! 3!)

₆C₃ = 6×5×4 / (3×2×1)

₆C₃ = 20

However, 2 of these combinations are lines, not triangles.

So there are 18 possible distinct triangles.

lhmarianateixeira

In this exercise we must observe the image given in the exercise and recognize how many triangles it has:

18 triangles

Then using the knowledge of combination we can calculate that there will be:

[tex]C_3 = 6! / (3! (6-3)!)\\C_3 = 6! / (3! 3!)\\C_ = 6*5*4 / (3*2*1)\\C_3 = 20[/tex]

However, 2 of these combinations are lines, not triangles. So:

[tex]20-2=18[/tex]

See more about triangles at brainly.com/question/25813512

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