That's incorrect, mathematically (this point is not arguable). Math doesn't care if you make your changes one at a time or billions at a time; the probabilities for achieving a desired sequence are the same.
To wit: fliping one coin at a time or flipping a billion coins at a time will have the same mathematical probabilities for achieving a specific 1 trillion length sequence of heads/tails.
However, what can change the above math is external bias.
The goal is to get for one winning hand to a marginally better hand. The hand is not dealt from scratch for each generation. Improvement is marginal and cumulative.
No one is arguing that all the possible permutations of a string with a given alphabet is not represented by an where a = the number of possible choices at a position and n is the length of the string.
However, as I explained earlier, if you are restricting the changes to only one character change at a time from the original source it is not calculated with a permutation nor a combination.
You will note that your statement above is referring to a specific target outcome rather than any outcome that can do the job. If you are looking for a single outcome from a single trial the probability will indeed be an. However that is not how evolution works.
Evolution will always *effectively* terminate the search when the first successful outcome is found *in that iteration* (read generation). Once that one of many possible successful outcomes is found the iteration stops. The next iteration will start with the new string as the origin with the probability of that state being 1.
There is more than a single specific outcome that can be considered successful so the probability is not 1/an but x>1/an. To calculate this probability we would need to know 'x' which is currently undetermined but definitely greater than 1.
Evolution also uses numerous concurrent trials which mean each member of the population has a probability of x>1/an. This means the probabilities of all members of the population during the current iteration is added together. Only if you are demanding a specific member of the population experience a specific mutation do you multiply them together.
This is where non-intelligently directed selection affects the probability calculation. All those organisms with a deleterious mutation will be removed from the population leaving the majority of the population with a neutral but potentially non-neutral mutation. The rest will have beneficial mutations. A single generation represents a single iteration so each generation will produce a separate iteration. If the fitness level you as an intelligent probability calculator have deemed as the target outcome has not been reached then the second iteration is added to the first. This will repeat until the fitness level is reached.
However Evolution cares not a whit what you or I claim for a satisfactory fitness target, it will mindlessly produce it's own.
At no time in all of this is the probability of a successful outcome 1/an as you postulate.