Question 124
For any set $A = \{a_1, a_2, \dots, a_m\}$, let $P(A) = a_1a_2\cdots a_m$. In addition, let $n = \binom{2010}{99}$ and let $A_1, A_2, \dots, A_n$ be all 99-element subsets of $\{1, 2, \dots, 2010\}$. Prove that $2011 \mid \sum_{i=1}^n P(A_i)$.