Acertain country's postal service currently uses 55-digit zip codes in most areas. how many zip codes are possible if there are no restrictions on the digits used? how many would be possible if the first number could not be 33?

a) 100000

b) 90000

Step-by-step explanation:

We have the possibility of 10 digits

(0,1,2,3,4,5,6,7,8,9)

If there are no restrictions on the digit, there are 10 possibilities for each of the five digits

We then have;

10*10*10*10*10

= 10^5

= 100000

This means 100000 zip codes are possible if there are no restrictions.

b) If the first digit cannot be 3, there are 9 possibilities. This is because the possibility of the first digit being 3 is 1 out of 10. Therefore the possibility of not being 3 is 9 out of 10

The other four digits have 10 possibilities each.

So we have

9*10*10*10*10

= 90000

This means there are 90000 zip codes if the first digit does not start with 3