# Math Help - [SOLVED] Permutation and Organized Counting

1. ## [SOLVED] Permutation and Organized Counting

hey guys can any1 help with this question its really confusing.

A Canadian postal code uses six characters. The first, third, and fifth are letters, while the second, fourth, and sixth are digits. A U.S zip code contains all 5 characters, all digits.

a) How many codes are possible for each country?

b) How many more possible codes does the one country have than the other?

a) Canada : 17 576 000
U.S : 100 000

b) 17 476 000

any idea how you get that answer?

2. Originally Posted by Nisar_0926
hey guys can any1 help with this question its really confusing.

A Canadian postal code uses six characters. The first, third, and fifth are letters, while the second, fourth, and sixth are digits. A U.S zip code contains all 5 characters, all digits.

a) How many codes are possible for each country?

b) How many more possible codes does the one country have than the other?

a) Canada : 17 576 000
U.S : 100 000

b) 17 476 000

any idea how you get that answer?
a)

(26 choices for each letter-26 letters in the alphabet, 10 choices for each number)

can you get the U.S answer now(10^5)?

b) subtract the U.S. from the Canada amount

3. yup i get b) now but for a) why do you multiply 26*10 3 times?

4. Originally Posted by Nisar_0926
yup i get b) now but for a) why do you multiply 26*10 3 times?
You have a six-digit/letter long code. The letters are the 1st,3rd, and 5th ( this is why i placed a 26 in each of those places - meaning there are 26 choices for each of these 3 spots) The numbers are the 2nd,4th,6th ( this is why i placed a 10 in each of these spots- meaning there are 10 choices for each of these spots ) now following the multiplicative principle i multiplied it to get the total amount.

5. Originally Posted by Nisar_0926
why do you multiply 26*10 3 times?
It really is $(26^3)(10^3)$; three letters and three digits.

6. how would you know when to use Factorials ! or power ^ to solve questions?

7. Originally Posted by Nisar_0926
how would you know when to use Factorials ! or power ^ to solve questions?
This is a hard question to answer unless looking at specifics. Factorials are generally used to find out how many times something can be arranged. For example the word "Factor" is 6 letters long, thus can be arranged 6! ways( instead of 26^6 which would be outrageous, we use 6! because we know which letter of the 26 represents each ). If the word factor had to start with f and end with r it could be arranged 4! times. If it is a question with more then one factor involved with numbers and letters such as the one I have solved, chances are it will be ^ and the multiplicative rule.

Does that make sense?