Question 1083912
.
The no. Of straight  {{{highlight(cross(line))}}} lines obtained by joining 16 points on a plane, no {{{highlight(cross(thrice))}}} three of them being on the same line is
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<pre>
= {{{C[16]^2}}} = {{{(16*15)/(1*2)}}} = 120. 


= the number of combinations of 16 points taken 2 at a time.
</pre>


On combinations,  read the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Combinations-.lesson>Introduction to Combinations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-combinations.lesson>PROOF of the formula on the number of Combinations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Problems-on-Combinations.lesson>Problems on Combinations</A> (*)

in this site.


By the way, in the lesson marked (*) you will find similar solved problem for planes in 3D . . . 



Also, you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic "<U>Combinatorics: Combinations and permutations</U>".