What is the number of bar code combinations?

Answer 1

Assuming you mean the 13 digit bar code and by "combinations" the mathematical permutations, then there are 1012 different bar codes - the 13th digit is a check digit based on the other 12.

On the 8 digit bar code there are 107 different bar codes - the 8th digit is a check digit based on the other 7.

"Combination" has a specific meaning in maths:

Permutations are sets arranged in order whereas Combinations are sets where order does not matter.

So for the six sets:

{1, 2, 3}, {2, 3, 1}, {3, 1, 2}, {1, 3, 2}, {2, 1, 3}, {3, 2 1}

they are different permutations of the digits 1, 2 & 3 (as the order changes each time) but the same combination (as each set contains one 1, one 2 and one 3 in some order).

The same is true of the six numbers: 123, 231, 312, 132, 213, 321

They are different permutations of the three digits 1, 2 & 3 but the same combination of them - each number contains one 1, one 2 and one 3.