2018 AMC 10A Problem 3

A unit of blood expires after 10!=10\cdot 9 \cdot 8 \cdots 1 seconds. Yasin donates a unit of blood at noon of January 1. On what day does his unit of blood expire?

\textbf{(A) }\text{January 2}\qquad\textbf{(B) }\text{January 12}\qquad\textbf{(C) }\text{January 22}\qquad\textbf{(D) }\text{February 11}\qquad\textbf{(E) }\text{February 12}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.