Car Tax Brain Teaser

[denis567]

I have taken this from a quarterly magazine I subscribe to, it is apparently devised by Group-Captain G Struan Marshall from Edingburgh.

"Odd place, Selenia," said Quaddie, helping himself to the whisky. "I was out there on a Government job last month; technical aid you know. I was sent out to advise them on budgetary policy. Found the Chancellor to the Treasury adding up car numbers"
"What on earth for?" I inquired.
"Road tax, you see, each number plate in the kingdom bears the digits 1 to 6, in some order. Zero is never used - it is a sacred symbol out there - and each digit on the plate must be different - like the king's toes"
"I beg your pardon"
Like the king's toes, he was born with six on each foot and is batty about their numerological significance. Well each car owner has to pay annually, a road tax of as many selenos as the number shown on his plate. For instance, if his number is 436521, then he must pay 436,521 selenos. Now that every possible number has been issued, the king wants to know how much the tax should bring annually"
"Quite a job, I should imagine"
"Not at all, I gave him the total in a couple of minutes"

How did he do it??

[Calibax]

For each digit, the average will be 3.5 (the mean of the numbers 1 to 6). so the average motorist will pay 3.5 x 100000 for the first digit, 3.5 x 10000 for the second digit... down to 3.5 x 1 for the sixth digit giving a total of 388,888.5.
Since every possible digit is issued there are 6 factorial (6x5x4x3x2x1) cars giving a total tax revenue of 388888.5 x 720 = 279,999,720 selenos