Correct Answer - Option 2 : 116
Concept:
The number of ways to select r things out of n things is given by \(\rm ^nC_r\)
\(\rm ^nC_r=\frac{n!}{(n-r)!\times(r)!}=\frac{n\times(n-1)\times....(n-r+1)}{r!}\)
Calculation:
To form a triangle we have to select 3 points out of 10 points,
∴Number of triangles that can be formed from 10 points = \(\rm ^{10}C_3=\frac{10\times9\times8}{3\times2\times1}\)
= 120
Also, the number of triangles that can be formed from 4 points = \(\rm ^4C_3=\frac{4\times3\times2}{3\times2\times1}\)
= 4
But, these 4 points are collinear and it is not possible to form a triangle out of these points.
∴ Number of triangles that can be formed with 10 points in a plane of which 4 are collinear
= 120 - 4
= 116
Hence, option (2) is correct.
