2019 Cayley Problem 24

Roberta chooses an integer r from the set \{2,3,4,5,6,7,8,9\}, an integer s from the set \{22,33,44,55,66,77,88,99\}, and an integer t from the set \{202,303,404,505,606,707,808,909\}. How many possible values are there for the product rst?

\textbf{(A)}\ 85\quad \textbf{(B)}\ 81\quad \textbf{(C)}\ 90\quad \textbf{(D)}\ 84\quad \textbf{(E)}\ 80

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.