2023 Pascal Problem 19

Ellie's drawer of hair clips contains 4 red clips, 5 blue clips, and 7 green clips. Each morning, she randomly chooses one hair clip to wear for the day. She returns this clip to the drawer each evening. One morning, Kyne removes k hair clips before Ellie can make her daily selection. As a result, the probability that Ellie chooses a red clip is doubled. Which of the following is a possible value of k?

\textbf{(A)}\ 6\quad \textbf{(B)}\ 9\quad \textbf{(C)}\ 12\quad \textbf{(D)}\ 4\quad \textbf{(E)}\ 13

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.