2017 Cayley Problem 24

Three coins are placed in the first three of six squares, as shown. A move consists of moving one coin one space to the right, assuming that this space is empty. (No coin can jump over another coin, so the order of the coins will never change.) How many different sequences of moves can be used to move the three coins from the first three squares to the last three squares?

\textbf{(A)}\ 44\quad \textbf{(B)}\ 40\quad \textbf{(C)}\ 42\quad \textbf{(D)}\ 48\quad \textbf{(E)}\ 50

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.