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Math Help - [SOLVED] Permutation and Organized Counting

  1. #1
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    Post [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?

    the answer for

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

    b) 17 476 000

    any idea how you get that answer?
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  2. #2
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    Quote Originally Posted by Nisar_0926 View Post
    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?

    the answer for

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

    b) 17 476 000

    any idea how you get that answer?
    a)

    canada = 26*10*26*10*26*10=17 576 000

    (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
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  3. #3
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    yup i get b) now but for a) why do you multiply 26*10 3 times?
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  4. #4
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    Quote Originally Posted by Nisar_0926 View Post
    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.
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  5. #5
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    Quote Originally Posted by Nisar_0926 View Post
    why do you multiply 26*10 3 times?
    It really is (26^3)(10^3); three letters and three digits.
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  6. #6
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    how would you know when to use Factorials ! or power ^ to solve questions?
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  7. #7
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    Quote Originally Posted by Nisar_0926 View Post
    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?
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