The correct answer is: excludes.
The word “excludes” means to leave out or not include. In this case, it means that it is impossible to create a method that will completely eliminate the possibility of error. This is because humans are fallible, and even the most carefully designed methods can be subject to mistakes.
The other options are incorrect because they do not accurately reflect the meaning of the sentence. The word “ignores” means to disregard or pay no attention to. The word “avoids” means to keep away from or prevent. The word “includes” means to contain or have as a part.
In conclusion, the correct answer to the question “You cannot devise a method which . . . . . . all possibility of error” is “excludes.” This is because it is impossible to create a method that will completely eliminate the possibility of error.