A) \[^{(n-p)}{{C}_{2}}\]
B) \[^{n}{{C}_{2}}-{{\,}^{p}}{{C}_{2}}\]
C) \[^{n}{{C}_{2}}-{{\,}^{p}}{{C}_{2}}+1\]
D) \[^{n}{{C}_{2}}-{{\,}^{p}}{{C}_{2}}-1\]
Correct Answer: C
Solution :
Given, total number of points = n and number of collinear points = p. We know that one line has two end points. Therefore total number of lines =\[^{n}{{C}_{2}}\]. Since p points are collinear, therefore total number of lines drawn from collinear points =\[^{\,p}{{C}_{2}}\]. We also know that, corresponding to the line of collinearity, one will also be added. Therefore number of lines = \[^{n}{{C}_{2}}\,-{{\,}^{p}}{{C}_{2}}+1.\]
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