if we assume that the password can only be 4 digits long, then for 7654 I get P = 1/5040 and unfortunately for 7656 its P=0
For my nephew who loves General Grievous:
Math checks out, assuming exactly 4 digits.
This number brings up lots of roofing contractors since dialing roof is 7663.
I looked for a good palindrome reference, but the best I could do was something shiny