Correct Answer - Option 2 : 69
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 line we have to select two points out of 13 points
∴Number of lines = \(\rm ^{13}C_2=\frac{13\times12}{2\times 1}\)
= 78
Also number of lines out of 5 points = \(\rm ^5C_2=\frac{5\times4}{2\times 1}\)
= 10
But, these 5 points are collinear, and only one line can be formed out of these points.
∴ The total number of straight lines obtained by joining these points in pairs
= 78 - 10 + 1 ....(We add 1, as one line can be obtained out of 5 collinear points).
= 69
Hence, option (2) is correct.