Question:
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is
(a) 45
(b) 40
(c) 39
(d) 38
Solution:
(b) 40
Number of straight lines formed by joining the 10 points if we take 2 points at a time $={ }^{10} C_{2}=\frac{10}{2} \times \frac{9}{1}=45$
Number of straight lines formed by joining the 4 points if we take 2 points at a time $={ }^{4} C_{2}=\frac{4}{2} \times \frac{3}{1}=6$
But, 4 collinear points, when joined in pairs, give only one line.
$\therefore$ Required number of straight lines $=45-6+1=40$