How to find the general term of this recurrence?

Question

$$\displaystyle a(n,r) = a(n,r-1) + a(n-1,r)$$

for $n,r >1$. Given that $a(1,0) = a(0,1) = 1$.

Answer 1

Clearly $a(n,r)$ is the number of ways to get from $(0,0)$ to $(n,r)$ by only moving one unit up or right on the lattice plain. So we have $a(n,r)=\binom{n+r}{n}$