Is there a formula to find a combination of numbers

[cubanopro]

Hi, what I meant in the title was:

Let's say that I have two variables in a game and I would like to know how many combination of numbers there is... For example if I have to calculate it for 3 times the possible combinations would be:
a,a,a
a,a,b
a,b,a
b,a,a
b,b,b
b,b,a
b,a,b
a,b,b

Is there a formula to calculate how many it would let's say for 13 times...or for 50 times.
Thanks in advance!
Rafael

 

[dodo]

If you replace a,b by 0,1, you will see that you have just enumerated all combinations for 3 binary bits, which are 2^3 = 8. If you want to repeat it 13 or 50 times, you will have 2^13 = 8192 or 2^50 = 1125899906842624. If you have three or four values instead of two, then you will have 3^n or 4^n cases.

(If you had 10 values, repeated 5 times, you would have 10^5 cases; the cases themselves are like the digits in a 5-digit number, from 00000 to 99999. Your example with a,b is the same as the digits in a 3-digit number in base 2, from 000 to 111.)

 

[cubanopro]

thank you very much Dodo you've been a great help!
You cannot answer my question in a better way. :)

Have a great day!
Rafael