Why do they need to be in one lineage. Each of these adaptations are locally advantageous and spread as such. The starch digestion (grain based diet), lighter skin, and the lactase persistence variants are no doubt present in many, if not most northern Europeans. Does this fit within your mathematical model? (At least two of these, skin and lactase, have been around for several thousand years, so consider the available population carefully.)
They don't have to be in a single lineage. But if you are going to make the argument that humans and chimpanzees evolved from a common ancestor, the total human population size over history allows for only a very few possible adaptive mutations to account for the reproductive fitness difference between humans and chimps. In addition, 99% of all humans that have ever lived have lived in the past 10,000 years. That doesn't leave you with much of a population to work with to do any kind of significant adaptation other than single adaptive mutations scattered throughout the population.
Most of the adaptations I and pitabread mentioned are not found in all of humanity so clearly multiple adaptive mutations can spread through the population at once without being contingent on one of the others being fixed. This is why you multiplication rule is not appropriate.
Fixation is not necessary for adaptation. In fact, evolutionary competition slows adaptation. You have two ways a lineage can get multiple adaptive mutations. One way is through DNA adaptive microevolution. That's demonstrated in the Kishony experiment. As a colony increases in size, mutant variants start to appear. When the colony reaches a size of about 1/(mutation rate) replications, there is a reasonable probability that an adaptive mutation has occurred (as well as mutations at every other site in the genome). That variant with the first adaptive mutation then has to start a new colony and as that new colony grows, the probability a second adaptive mutation improves, and when that second colony achieves a population of about 1/(mutation rate) replications, you have a good probability that one of the members of that colony with the first adaptive mutation will get a second adaptive mutation. This new more fit variant must then form a third colony and the cycle repeats. Note that in this process, new alleles are being produced at each adaptive step.
The other way adaptive mutations can accumulate in the lineage is recombination. One parent with an allele that has an adaptive mutation recombines with the other parent that has a different allele with a different adaptive allele to give an offspring with both adaptive alleles. In this new alleles are not being produced. With a breeding program or environmental conditions which select for particular variants to increase the frequency of those variants with adaptive alleles, the process can work pretty rapidly. If the recombination process is random (as with HIV and pollination), it is governed by the trinomial distribution. The math is trivial, so you wouldn't be interested.
The video is about bacteria, as you well know since you posted it.
Sure, but DNA is DNA. You have to take into account the ploidy. Each human replication is 2 genome replications. And of course, take into account recombination. It is possible that in the recombination process, the adaptive allele is not passed to the offspring. You are aware that doubling the number of genome replications does not double the probability of an adaptive mutation occurring?
How big do you think the Inuit population has been in the last 10,000 years? How many adaptions do you expect from a population of that size? Let's see that model predict something.
I have no idea of the number of Inuit that have ever lived. From Wikipedia:
Inuit - Wikipedia
There are Inuit populations in Europe, United States, Canada, Greenland, and related ethnic groups from Asia and who knows how many in the past and where. If there were a billion people in that lineage, that would be enough genome replications to give about 1 mutation at every site in the genome. Depending on when the adaptive mutation occurred, the frequency of that variant could increase over generations improving the probability of a recombination event with another parent with a different adaptive allele. As I estimated earlier, this lineage might accumulate 5-10 adaptive mutations for various selection conditions (diseases, diet, thermal stress, etc.) When it comes to creating new alleles, it is all about replication because that's when you have a possibility of a mutation occurring, some will be detrimental, some will be neutral, and on rare occasions, adaptive.
The Inuit aren't bacteria. Neither are any other human group.
Starvation puts selection pressure on humans and bacteria alike. Humans have adapted to it by farming. What adaptation mutations give humans the capability to farm and chimpanzees can't.