Actually, if I'm reading the OP correctly, they already have the 7 unique tiles and want to know how many possible combinations they can make from them, which would be 7!
If you replace one with a blank, the number of combinations depends on the rules for the blank. If the blank can only be one of the remaining letters, then the number of combinations becomes 7! * 20. If, however, the blank can be any letter, including any of the other 6 chosen, the formula becomes more complex, as you would have 7! * 26 minus any duplicates (I haven't worked out how to calculate the number of duplicates that would be involved).