if you had an 8 digit code with the numbers 0 to 9 how many possible combinations would there be?

Answer 1

Simple anwser:
99999999 +1 = 100,000,000

Technical answer:

For any possible code the number of combinations is A^n (A to the n) where A is the number of possible states for each digit and n is the number of digits in the code.

For example, in binary A can have two states 0 and 1. In the base ten number system A has 10 possible states, 0-9.

As your code is 8 digits long, you have 10^8 possible combinations.

In your question the answer is particularly easy as 0-9 is the number system we use in day to day life. You simply can write out eight nines (99,999,999) and add 1 (for the 00000000 possibilty) and get 100,000,000. Which is 10^8.

This assumes you can re-use numbers. If you can not re-use numbers (as in a numbered ball lotery, for example) then Clash is correct.

Answer 2

Ok, if you are talking about true mathematical combinations then the order of the numbers doesn't matter so 12345678 is the same as 65478231 because they use all the same numbers.

To determine combinations you can use a calculator and you find that picking 8 things out of ten without looking at order means you have 45 combinations. (There is a nCr function on my calculator to find combinations.)

If the order matters, and you can repeat numbers in the 8 digit code do the following:
The first digit has 10 different ways to be picked, the 2nd number has 10 different ways to be picked, the 3rd number has 10 different ways to be picked....so
10x10x10x10x10x10x10x10 = 10^8

If the order matters, and you can not repeat digits, do the following:
The first number has 10 different ways to be picked, the second number has 9 ways to be picked, the 3rd one has 8 ways to be picked....so
10x9x8x7x6x5x4x3 = 604800

Hope some of this makes sense. Good Luck.

Answer 3

0 to 9 is 10 digits. So how do you have an 8 digit code with digits 0 to 9?

Answer 4

It is 10^8 (100,000 000) if the first digit is allowed to be a zero. (all landline telephone codes start with 0 in the UK)

If it isn't allowed to be a zero, that eliminates:
10,000,000 codes starting with 0 or 00 or 000 etc and the answer would be 9 x 10^7 (90,000,000) (bank account codes are 8 digits and never start with 0 in the UK)

Answer 5

Big Daddy, can you help me with the code for the same question except my permutations are from 8 known digits (0,0,1,2,5,8,9,9) with a 6 digit code? I think the number of permutations are 20,160. NpK = 8!/(8-6)! = 20,160. Out of these combinations, I want to avoid the permutations that are a "waste" i.e. no 3, 4, or 6,7 numbers need be generated. Does that make sense?

Answer 6

10^8

Answer 7

10^8

or

10 times itself 8 times.

Answer 8

There would be 10^8 possible combinations. Are there supposed to be any restrictions, like you can only use each one once?

Answer 9

With or without repetition?

If repetition is allowed, 10 for first digit, times 10 for second, times 10 for the third.....

Answer 10

8
C =10!/(2!*8!)=9*10/2=45
10