The number of combinations with 7 unique letters is not 7!, unless you simply are trying to arrange 7 unique tiles that already have been chosen. However, I understood the OP's question to involve 7 unique tiles, chosen from a total of 26 possible letters, which gives a different equation. That equation would be 26 * 25 * 24 * 23 * 22 * 21 * 20. Your first tile could be one of 26 possible letters. Since repeats were excluded, the next tile could only have 25 possibilities - the first chosen letter is "taken". And so on. This equation becomes (A!)/(A-n)!, where the variables are as I described above.

If the blank tile can be *any* letter, including ones that have already been chosen, then you simply multiply by 26, as many times as you've got blank tiles. If the blank tile must also be unique, the it works a though it were just another tile with a letter on it.

When the tiles can all be chosen without regard to whether there is repetition (or when they're all blank), the equation becomes simply A ** n, where A is the size of the alphabet, and n is the number of tiles.