Constraint-prof V balakrishnan video

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https://www.youtube.com/watch?v=http://m.youtube.com/watch?v=8X1x9RLaaxc

he tells number of contraints (he write no of pairs ) is nC2 how is it, i didn'tunderstand!
 
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Its in the 6 to 7th minute of video
 
I didn't post there because while asking question itself i made mistake and after posting i released my correct was the above one and no that one.so only i did it.i didn't knew how to delete it.
 
He writes explicitely a question mark over the equal sign, and then goes on to prove that it can't be correct, because you get an absurd answer (the number of degrees of freedom cannot be negative). The conclusion is that the number of constraints is not ##n\mathrm{C}2##.
 
I know that he is un proving and i understand it.but what i didn't get was .nc2 how it came?
 
##N\mathrm{C}2## is the number of pairs of particles in a set of ##N## particles. What is it you don't get?