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mathmath333
 one year ago
Counting Problem
mathmath333
 one year ago
Counting Problem

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1\(\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}}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2is the answer \(\dbinom{6}{2} + 6*4\) ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2right, both are same just a +1 is missing in my earlier reply

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2forget about 4 collinear points

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2then you have 6 points, you know that any two points determine a line so how many lines can you make using 6 points ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2next, from each of these 6 points, you can draw a line to each of the 4 collinear points, yes ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2dw:1440183836929:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2how many lines can you draw from those 6 points to those 4 collinear points ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2dw:1440183971999:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2nope, notice that from each of those 6 points, you can draw exactly 4 lines to those collinear points

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Yes, so far the count is \(\dbinom{6}{2}+4*6\) can you guess the one line that is missing ?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1dw:1440184361598:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2so the final answer is \(\dbinom{6}{2} + 6*4+1\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2your textbook answer counts it in a different way
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