How many different ways can you distribute $5$ apples and $8$ oranges among six children if every child must receive at least one piece of fruit? If there is a way to solve this using Pólya-Redfield that would be great, but I cannot figure out the group elements.
I know this is a duplicate of: How many different ways can you distribute 5 apples and 8 oranges among six children?. But I can not comment on this or contact the member who explained the task.
Could someone explain in more detail how to apply this, especially how to evaluate the sums?
Maybe someone has more examples? Or even a book with solved exercises? The main Problem is i dont know what i need to know in order to apply it.
Application 1: How many distinct circular necklace patterns are possible with n beads, these being available in k colors.
It could be solved by Burnside's lemma but I also have no clue to to apply it.