Currency Collector

Question

You are in a foreign country that has $r$ distinct denominations of currencies. The denominations are $c_1 < c_2 < \dots < c_r$. You have $n_i$ bills of denomination $c_i$ in a bowl. You select $1 \leq k \leq \sum_{i=1}^r n_i$ bills from the bowl uniformly at random without replacement. Find the expected amount of money that you grabbed with $r = 9, c_i = i, k = 9,$ and $n_i = 10-i$.