2006 AMC 10A Problem 18

A license plate in a certain state consists of 4 digits, not necessarily distinct, and 2 letters, also not necessarily distinct. These six characters may appear in any order, except that the two letters must appear next to each other. How many distinct license plates are possible?

\mathrm{(A)}\ 10^4\times26^2\qquad\mathrm{(B)}\ 10^3\times26^3\qquad\mathrm{(C)}\ 5\times10^4\times26^2\qquad\mathrm{(D)}\ 10^2\times26^4\qquad\mathrm{(E)}\ 5\times10^3\times26^3

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