Pretty sure that it's 7! (7 factorial), which would be 7*6*5*4*3*2*1, though I could definitely be wrong. It's been about 11 years since I did any of this stuff.
If you wanted to see how many ways you could arrange it while keeping, say, 2 numbers constant, it would be 7! divided by 2!, iirc.
Huge grain of salt here, though, as I said.
EDIT: I see above that I was correct. However, it goes to show you that I'm getting stupidererer as I age, since I took 7imz's "7!" as an exclamation (i.e., "OMG, IS IT SEVEN!?") rather than as 7 factorial (or 7-bang, as we used to say in soph year of HS ).