Consider a system of 10 (say) point particles each at a fixed distance from each other in 3-D space.
In this case, the number of degrees of freedom: $3*(number-of-particle)-\binom{10}{2}=3*10-45<0$
which is wrong as it cannot be negative.
So, is the number of degrees of freedom 6 by considering it a rigid body?
If yes, why does the above formula fail?
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