There are 10 points on a sheet of paper, and no three of them lie on the same straight line. How many different straight lines can be drawn so that each line passes through two of these points?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 45
A straight line is fixed by any 2 points; when no three points are on one line, every pair gives a different line, so the count is \(^nC_2\).
Points \(n=10\)
Lines \(\displaystyle =\,^{10}C_2=\frac{10\times9}{2\times1}=45\)
Why the other options are incorrect
Option (1) 90 — Incorrect. This is \(^{10}P_2\), which counts the line through P and Q again as the line through Q and P.
Option (2) 100 — Incorrect. This is \(10\times10\), which even pairs a point with itself.
Option (4) 20 — Incorrect. This is \(10\times2\), which is not a counting rule.