+0  
 
0
134
3
avatar

Prove combinatorially that (10 choose 4) = (9 choose 3) + (9 choose 4)

 Mar 15, 2021
 #1
avatar+33795 
+1

10 c 4 =   10! / (4! 6!) = 210

 

9 c3 = 9! / (3! 6!) = 84

9 c 4 = 9!/ ( 4! 5!) = 126       126 + 84 = 210

 Mar 15, 2021
 #2
avatar
0

Is there a way to do this without calculating it? Through combinitoric means?

Guest Mar 15, 2021
 #3
avatar+201 
0

we have the hockeystick identity which gives you instantly the answer

 

we can prove the hockeystick identity by using trianglular numbers

jxc516  Mar 16, 2021

9 Online Users