2005
Problem - 1777
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?
It is equivalent to counting the number of selecting $7$ distinct numbers from $8$ choices because each selection has just one way to form an increasing sequence. Hence, the result is $C_8^7=\boxed{8}$.