Counting Problem

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\(\large \color{black}{\begin{align} & \normalsize \text{There are \(10\) points in a plane of which \(4\) are collinear. }\hspace{.33em}\\~\\ & \normalsize \text{No other \(3\) points are collinear.}\hspace{.33em}\\~\\ & \normalsize \text{Find the number of lines that can be drawn .}\hspace{.33em}\\~\\ \end{align}}\)
is the answer \(\dbinom{6}{2} + 6*4\) ?
10C2-4C2+1

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Other answers:

right, both are same just a +1 is missing in my earlier reply
how u got that
forget about 4 collinear points
then you have 6 points, you know that any two points determine a line so how many lines can you make using 6 points ?
6c2
next, from each of these 6 points, you can draw a line to each of the 4 collinear points, yes ?
yes
|dw:1440183836929:dw|
how many lines can you draw from those 6 points to those 4 collinear points ?
6C4
|dw:1440183971999:dw|
nope, notice that from each of those 6 points, you can draw exactly 4 lines to those collinear points
4*6
Yes, so far the count is \(\dbinom{6}{2}+4*6\) can you guess the one line that is missing ?
|dw:1440184361598:dw|
Thats it!
so the final answer is \(\dbinom{6}{2} + 6*4+1\)
ok thnsk
your textbook answer counts it in a different way

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