Provide a combinatorial argument for the given equation $${^{n+1}C_4}= {{^{^{^nC_2}}C_2}\over 3} \text{, for } n\ge 4$$
HINT: Consider a group of $n+1$ terms of which one is considered special. Argue that both sides of the above identity represent the number of subsets of size $4$.
I get how the LHS is the number of size $4$ subsets of a set of $n+1$ terms. How does the RHS follow suit?