Question

there are 4, 6, and 7 points on three lines. How many triangles is it possible to create with given points as vertices?

Answer 1

4 triangles can be created with 3 points on a line.

20 triangles can be created with 6 points on a line.

30 triangles can be created with 7 points on a line.

Combination has to do with selection.

Note that a triangle has 3 vertices. If there are 4 points on a line, the number of triangles it is possible to create is derived using the combination formula shown as:

$nC_r=\frac{n!}{(n-r)!r!}$

$4C_3 = \frac{4!}{(4-3)!3!}\\4C_3 =\frac{4\times3!}{3!}\\4C_3=4triangles$

This means that 4 triangles can be created with 3 points on a line.

For a line with 6 points:

$6C_3 = \frac{6\times 5\times 4\times 3!}{(6-3)!3!}\\6C_3 =\frac{6\times5\times 4\times3!}{3!3!}\\4C_3=20triangles$

This shows that 20 triangles can be created with 6 points on a line.

For a line with 7 points:

$7C_3 = \frac{7\times 6\times 5\times 4!}{(7-3)!3!}\\4C_3 =\frac{7\times6\times 5\times4!}{4!3!}\\4C_3=30triangles$

This shows that 30 triangles can be created with 7 points on a line.

Learn more here: brainly.com/question/23885729