[INST] What is the sum of all integer values n for which C(20,n)+C(20,10)=C(21,11)?/n [/INST]  ###Response: From Pascal's identity C(n-1,k-1)+C(n-1,k)=C(n,k).

Therefore, we have C(20,11)+C(20,10)=C(21,11), so n=11.

We know that C(21,11)=C(21,21-11)=C(21,10).

We use Pascal's identity again to get C(20,9)+C(20,10)=C(21,10), so n=9.

There are two values for n, 9 and 11, so the sum is 9+11=20.