There are 15 points in a plane, no two of which are in a straight line except 4, all of which are in a straight line. The number of triangles that can be formed by using these 15 points is

There are $15$ points in a plane, no two of which are in a straight line except 4, all of which are in a straight line. The number of triangles that can be formed by using these $15$ points is

A
404
B
415
C
451
D
490

Solution:

The required number of triangle is

$^{15} C_{3} -^{4} C_{3} = 455 - 4 = 451$

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