# Logic behind the number of combinations of numbers

## Main Question or Discussion Point

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.

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.