2015 AMC 8 Problem 10

How many integers between 1000 and 9999 have four distinct digits?

\textbf{(A) }3024\qquad\textbf{(B) }4536\qquad\textbf{(C) }5040\qquad\textbf{(D) }6480\qquad \textbf{(E) }6561

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