Well an IP is in the format:
xxx.xxx.xxx.xxx
where xxx can be between 0 and 255. That is 256 numbers soooooo the answer is 256^4. Which is, ummm, 4294967296.

In IP v7 or whatever version is next there will be six lots of 3 numbers, ie xxx.xxx.xxx.xxx.xxx.xxx, which gives umpteen million address to every square meter of the planet. lol.