The best way to think of this is how many options there are for each letter. There are 7 possibilities for the first letter. Then there are 6 possibilities (out of the remaining letters) for the second latter. Then 5 possibilities for the next, and so on. The total number of possibilities will be 7x6x5x4x3x2x1, which equals 5,040. So there are 5,040 different ways to arrange 7 letter words.
