2020 Pascal Problem 24

Lucas chooses one, two or three different numbers from the list 2, 5, 7, 12, 19, 31, 50, 81 and writes down the sum of these numbers. (If Lucas chooses only one number, this number is the sum.) How many different sums less than or equal to 100 are possible?

\textbf{(A)}\ 43\quad \textbf{(B)}\ 39\quad \textbf{(C)}\ 42\quad \textbf{(D)}\ 40\quad \textbf{(E)}\ 41

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 Pascal contests here.