First slide

Combinations

Question

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

Moderate

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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