0
$\begingroup$

When they were first introduced, postal zip codes were five digit numbers, theoretically ranging from $00000$ to $99999$. (In reality, the lowest zip code was $00601$ for San Juan, Puerto Rico; the highest was $ 99950$ for Ketchikan, Alaska.) An additional four digit have been added, so each zip code is now a nine digit number. How many zip codes are at least as large as 60000-0000, are even numbers, and have a $7$ as their third digit?

Attempt: $A1*A2*A3*...*A9$ be a zip code. With $A3 = 7$. I don't know how to continue.

Can someone please help me with this problem? Thanks

$\endgroup$
1
$\begingroup$

To be at least as large as 60000-0000 the first place must be one of 6,7,8,9.

To be an even number, the last place must be one of 0,2,4,6,8.

For the third place to be 7 there's only one choice for the third place. 7

The remaining six places can each be any of the ten digits, 0,1,2,3,4,5,6,7,8,9.

Each place is selected independently (digits can be repeated).

Count the ways to do this.

$\endgroup$
  • 1
    $\begingroup$ So the total N = 4*10*1*10*10*10*10*10*5 ? $\endgroup$ – user3459 Sep 30 '14 at 0:44

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.