1. The problem statement, all variables and given/known data Give two proofs (algebraic and combinatorial) of the following formula: ((nchoose2) choose 2)=3(n choose 3) +3(n choose 4) 2. Relevant equations 3. The attempt at a solution Alright, I have part of the algebraic one but I get stuck, also I don't know how to approach the combinatorial proof... so any suggestions would be great... Algebraic proof: 3(n choose3) +3(n choose 4) is equal to: 3((nchoose3) +(nchoose4)) and by the additive property that equals: 3((n+1 choose 4) which is equivalent to: (n+1)(n)(n-1)(n-2)/8 This is where I get stuck.... i know that (n)(n-1)/2 equals n choose 2 but then that leaves me with: (n choose 2)((n+1)(n-2)/4) any help would be great!!!