Degrees of Freedom for Rigid Body of n Particles

[ajayguhan]

How is for rigid body made up of n particle, the degree of freedom is 3n-nC₂.i can understand that degree freedom of n particle is 3n and suppose you have 2 particle whose distance between them is fixed, then degree of freedom is n 3(2)-1=5.if we have three particles then it is 7.
Therefore n particle whose distance between them is fixed have degree of freedom which is 3n-(n-1) .how can it be 3n-.nC₂.

 

[UltrafastPED]

What is C₂?

 

[voko]

It does not matter how many particles a rigid body is made of (except when all of them are collinear). It always has 6 degrees of freedom. 3 rotational (Euler angles), and 3 translational. All-collinear rigid bodies, even though the term "body" is hardly applicable here, lose one rotational DoF.