AMC 10 2020b Problem 5

How many distinguishable arrangements are there of $1$ brown tile, $1$ purple tile, $2$ green tiles, and $3$ yellow tiles in a row from left to right? (Tiles of the same color are indistinguishable.) $\textbf{(A)}\ 210 \textbf{(B)}\ 420 \textbf{(C)}\ 630 \textbf{(D)}\ 840 \textbf{(E)}\ 1050$