Discussion
Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. How many straight lines, including the first two, can be formed with these points?
Answer: D
A line needs two points. Two points on the same line give nothing new - they just re-describe that line.
One point from each line:
\[ 6 \times 5 = 30 \text{ new lines} \]
The two original lines add 2 more.
\[ 30 + 2 = 32 \]
Taking \( {}^{11}C_{2} = 55 \) would count every pair, including the \( {}^{6}C_{2} + {}^{5}C_{2} = 25 \) collinear pairs that produce no new line - and \( 55 - 25 + 2 = 32 \) again.
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