Expected largest label among ten drawn from twenty

A box contains $20$ balls numbered $1$ to $20$. You draw $10$ of them at random without replacement. What is the expected value of the largest number drawn?

$210/11$. $P(\max=k)=\binom{k-1}{9}/\binom{20}{10}$, and the hockey-stick identity collapses $\sum_k k\binom{k-1}{n-1}$ to $n\binom{N+1}{n+1}$. Hence $E[\max]=\tfrac{n(N+1)}{n+1}=\tfrac{10\cdot21}{11}$.