number combinations?

Question

how many diffrent number combinations can you make with the nuber 1-56???

Answer 1

The answer to your question depends on the length of the sequence that you're interested in, but the general relationship looks like this:

C = N^s, where

N = the range of numbers available to the sequence
s = the length of the sequence (i.e. the amount of numbers)
C = number of possible combinations

For example, a 3 digit sequence using only the numbers 0 and 1 has 8 possible combinations (2^3 = 8).

For the case that you mentioned, N = 56, but for the value of s, let's use a real-life example. Your question is probably out of curiousity in regards to a lottery or something like that, so I'll use the Powerball jackpot as an example. A Powerball ticket requires that a person pick 6 numbers, so the number of combinations to choose from would be:

C = 56^6 = 30,840,979,456 combinations

Yeah, that's 30+ Billion......which makes it even more remarkable that there are any lottery winners at all.

Answer 2

56 choose 1 +
56 choose 2 +
::
56 choose 56