Question:
How many triangles can be obtained by joining 12 points, four of which are collinear?
Solution:
Total number of points on plane = 12
Triangles can be formed from these points $={ }^{12} \mathrm{C}_{3}$
= 220
But 4 points are colinear, the number of triangles can be formed from these points
$={ }^{4} \mathrm{C}_{3}$
= 4
We need to subtract 4 from 220 because in the formation of triangles from 4 colinear points are added there.
So no of triangle formed is $=220-4$
= 216
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