In a plane, there are 9 points, out of which 4 are collinear. The number of triangles made by these points is:

Total points in the plane = 9

Points that lie on the same line = 4 (collinear)

Remaining points = 5 (not on that line)

To form a triangle, 3 points are needed that are not all on the same line.

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Total ways to select any 3 points from 9 points:

$C(9,3) = \dfrac{9!}{3! \times 6!}$

$C(9,3) = \dfrac{9 \times 8 \times 7}{3 \times 2 \times 1}$

$C(9,3) = \dfrac{504}{6}$

$C(9,3) = 84$

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If 3 points are selected from the 4 collinear points, they will all be on the same line and will not form a triangle.

Number of ways to pick 3 points from the 4 collinear points:

$C(4,3) = \dfrac{4!}{3! \times 1!}$

$C(4,3) = \dfrac{4}{1}$

$C(4,3) = 4$

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Number of triangles = Total combinations - Combinations that don't form triangles

Number of triangles $= 84 - 4$

Number of triangles $= 80$

Therefore, the number of triangles that can be formed is 80.