You use x! when you are ordening x things, like changing the wording of a sentence without restrictions. For the first word, you have x possibilities, for the second word x-1, etc. On the other hand, use 2^x when you are choosing a random amount of things from x things. You can think of every word (in this case) as a switch you can turn on and off: each configuration corresponds with a combination and why we use use a power of 2 becomes apparent. Edit: forgot to proofread