Prove combinatorially that (10 choose 4) = (9 choose 3) + (9 choose 4)
10 c 4 = 10! / (4! 6!) = 210
9 c3 = 9! / (3! 6!) = 84
9 c 4 = 9!/ ( 4! 5!) = 126 126 + 84 = 210
Is there a way to do this without calculating it? Through combinitoric means?
we have the hockeystick identity which gives you instantly the answer
we can prove the hockeystick identity by using trianglular numbers
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