Prioritizing Stories

You cannot answer that question with this information. Prioritization by the Product Owner and Sprint Goal are more important.

I don't agree that this question can't be answered. It definitely can be, if you make a few assumptions. If you assume that the Product Owner has properly ordered the Product Backlog based on not only stakeholder needs, but also working with the Development Team on technical dependencies or risks and the order accounts for this and you also assume that the capacity of the Development Team has been consistent over the past Sprints and will continue to remain consistent, you can make some starting suggestions on what work the team should take on.

The first thing I would do is apply Yesterday's Weather. I would not be looking at all 6 Sprints, but the last few. Some people suggest up to 5, but I prefer 3. Looking at the average velocity of the last 3 Sprints, you would see that the average velocity for the team is 26 Points. Therefore, the team should not plan on bringing in more than 26 Points into the current Sprint. Looking at the four options presented, all four come in at less than 26 Points, so that's good.

In terms of pure value, the best option would be the second option (Stories 1, 2, 3, 4, 5, 6, 8). This option presents the most stories from the top of the backlog down. This is assuming that Story 7, 9, or 10 wouldn't be a technical dependency for one of those.

How I would advise the Product Owner to prepare for Sprint Planning would be to look at those 7 Stories. From there, I would try to craft a cohesive Sprint Goal. This Sprint Goal doesn't have to include all 7 Stories, and I would go so far to to advise against a goal that would require all those Stories to be delivered. I would expect the Product Owner to go in with an idealized Sprint Goal and the Product Backlog Items needed to support that.

However, Sprint Planning is a discussion between the Product Owner and the Development Team. There could be very good reasons why the Development Team doesn't select particular stories. It is important to realize that selecting stories based on Velocity and the Product Backlog is against the pull model where the Development Team pulls work and is more like a command-and-control model rather than collaboration between stakeholders. The best that you can get going in is a rough idea of what is feasible so the Product Owner can come in with somewhat realistic espectations to help guide the discussion.

When I don't consider al the elements that you need in real life, but just take the average velocity vs stories, then the 1, 2, 3, 4, 5, 6, 8 should be the correct answer.

You cannot answer that question with this information. Prioritization by the Product Owner and Sprint Goal are more important.

I agree.

Unfortunately this questions seems to have reduced product ownership to a mathematics exercise.

I also disagree with the premise that a team should bypass a higher prioritized item, in favour of a smaller one, just to maximize the forecast number of story points.

If Story 7 is so large, and there is a risk that it won't be completed within a sprint, couldn't it also be an effective use of the upcoming sprint to address this, such as by splitting the story (and completing part of it), or conducting an experiment or investigation to increase the likelihood of it being delivered in a later sprint.

I'm in the "this can't be answered" camp.  The answer comes from the Development Team during Sprint Planning based on information that is known at that time and the discussions that occur within the Scrum Team.  Past performance and previous estimates will provide data for the decisions but there is no formula that can make that decision. 

There is a lot of information missing such as:

• are they any dependencies between stories?
• will the individuals needed be available when needed?
• are there any holidays during the next sprint?

All you have is past information stated in that question.  There is nothing about future mentioned so you are not taking all information into account. 

which combinations should they try and include in the next sprint?

If that's really become the challenge, why would they Sprint at all?

Outside above mentioned advices (which are all great), I can highly recommend reading the Professional product Owner by Don McGreal and Ralph Jocham and Product Mastery by Geoff Watts. There are multiple tactics and inspirational stuff in these books and helped me personally to get a better understanding of product ownership.