- #1
dancergirlie
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Homework Statement
Give two proofs (algebraic and combinatorial) of the following formula:
((nchoose2) choose 2)=3(n choose 3) +3(n choose 4)
Homework Equations
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!