2005 AMC 10B Problem 18

All of David's telephone numbers have the form 555-abc-defg, where a, b, c, d, e, f, and g are distinct digits and in increasing order, and none is either 0 or 1. How many different telephone numbers can David have?

\mathrm{(A)} 1 \qquad \mathrm{(B)} 2 \qquad \mathrm{(C)} 7 \qquad \mathrm{(D)} 8 \qquad \mathrm{(E)} 9

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