AMC 8 2020 Problem 7

How many integers between $2020$ and $2400$ have four distinct digits arranged in increasing order? (For example, $2347$ is one integer.) $\textbf{(A) }\text{9} \textbf{(B) }\text{10} \textbf{(C) }\text{15} \textbf{(D) }\text{21} \textbf{(E) }\text{28}$