The image you've uploaded contains a series of math problems related to combinations, permutations, and routes in geometry. Here’s a summary of the tasks shown in the document:

OPGAVE 1 (Task 1):

• a) The question asks how many ways Anne can arrange 51 books.
• b) The books are sorted into categories based on color and position. The question asks how many ways the books can be arranged based on these conditions (15 red books, 14 green books, etc.).

OPGAVE 2 (Task 2):

• a) Vicky is rolling 8 dice, and the task is to calculate how many possible outcomes there are.
• b) Vicky rolls the dice and the question asks for the number of possibilities to get a sum of 5.

OPGAVE 3 (Task 3):

• a) This is a route optimization problem asking how many shortest routes there are from point A to C.
• b) This asks for the number of shortest routes from point A to B via point P.

Would you like help solving one of these specific questions, or would you like to go over all the problems one by one? Let me know if you have a particular focus!

If you'd like a deep dive into any of these, feel free to ask for more details!

Here are some related questions for further exploration:

1. How do we calculate the total number of arrangements of objects when some items are identical?
2. What is the concept of a combination, and how does it differ from a permutation?
3. How do you calculate the number of possible outcomes for a combination of events (like rolling dice)?
4. What is the shortest path problem, and how is it solved in graph theory?
5. Can we apply the binomial coefficient to solve problems involving dice rolls or book arrangements?

Tip: When dealing with problems involving repeated items (like identical books), use the formula for permutations of multiset objects:
$\frac{n!}{k_1! \cdot k_2! \cdot \ldots \cdot k_r!}$