Logic behind the number of combinations of numbers

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Discussion Overview

The discussion revolves around understanding how to calculate the number of combinations for a 4-digit code using the digits 0-9. Participants explore the reasoning behind the multiplication of choices rather than addition, and seek clarity on the underlying logic.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant asks how to determine the number of combinations for a 4-digit code using digits 0-9.
  • Another participant suggests that the calculation involves multiplying the number of choices for each digit, resulting in 10 x 10 x 10 x 10 = 10,000 combinations.
  • A different participant expresses confusion regarding the multiplication method, questioning why addition is not used instead.
  • Further elaboration is provided by another participant, detailing the choices available for each digit and illustrating the total combinations through a breakdown of possibilities.
  • One participant proposes using a tree diagram to visualize the combinations of numbers.

Areas of Agreement / Disagreement

Participants express differing levels of understanding regarding the multiplication method for calculating combinations, indicating that there is no consensus on the reasoning behind the approach.

Contextual Notes

Some participants' contributions include assumptions about the structure of the problem and the method of calculation, which may not be universally accepted or understood.

lntz
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Hey,

so i think this is a fairly simple question but i'd like to get it firmly understood in my head.

How do you figure out the amount of combinations of digits in say a 4 digit code. with numbers 0-9...

I can't think of a good way to say it, but for example you could have 0,1,2,3 or 1,2,3,0 etc etc.

So how do you figure out quickly just how many combinations exist.


Thanks for any help you give
 
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Ten choices for the first number, ten choices for the second number...: 10 x 10 x 10 x 10 = 10,000

All of the numbers between 0000 and 9999.
 
Sorry my maths is lacking... why do you multiply the numbers, and not add them.
 
0 thru 9, or 10 different choices, for each digit.

00, 01, 02, 03...09 10 choices
10, 11, 12, 13...19 10 choices
20, 21, 22, 23...29 10 choices
...
30 thru 89... 60 choices
...
90, 91, 92, 93...99 10 choices
total 100 choices

000,001,002...099 100 choices
100,101,102...199 100 choices
...
200,201,202...899 700 choices
...
900,901,902...999 100 choices
total= 1000 choices

Do the same thing for the next digit...
 
It might help to imagine a tree diagram, with all the possibilities the numbers could be.
 

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