How many combinations of 15 digits can me made?

JohnnyBiggles

Just some random thought surrounding the whole Target issue had me thinking about numbers. I believe the number was around 40M card numbers were compromised and I thought, "What if they had to cancel all of those and reissue cards to that many people? What eventually becomes of those card numbers and how big is the pool of used/unused numbers?"

Considering the first digit of each of the cards issued is static (usually represents the company of the distributing card), how many combinations of 15 digits are there if zeros and number repeats are allowed? What is the formula? I've seen x to the power of y and factorial when this was asked but what is the actual way of going about getting that answer, and what is the answer?

Vask3n

I think the approach to this would be:

There are 10 possibilities for each digit (0-9). If numbers and repeats are allowed you would have 10 ^15. If you could not reuse numbers I think that's when you would use factorial.

JohnnyBiggles

Wow that's 1 Quadrillion. The pool is BIG! Thanks!

EdTheLad

Yes 10^15, if no repeats were allowed you would need a larger number pool.
For example if the lottery was 6 numbers with a pool of 40, chances to win would be:

6/40 x 5/39 x 4/38 x 3/37 x 2/36 x 1/35 = 720/2763633600 = 0.00000026052658
= 3,838,380 to 1 chance

swild

The first four digits are generally reserved. Heres an article that explains it fairly well.
HowStuffWorks "Credit Card Numbers"