Sunday, 8 May 2016

combinatorics - Combinatorial proof of nchoosepnchooseq=sumnk=0nchooseknkchoosepknkchooseqk

I am trying to do a combinatorial proof of (np)(nq)=nk=0(nk)(nkpk)(nkqk)



For the left side. I thought of two urns with n red and n blue balls and choosing p-red balls and q-blue balls.



For the right side, i am not very sure, but I thought of make k the number of couples of red and blue balls. Making this is (nk) ways. Since it's the same counting (nk) or (nnk). I choose (nkpk) red balls and the same way with blue.




But I do not think this is right, any help will be appreciated.

No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find lim without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...