For the following question:
"A teacher has 10 different books that she wants to distribute to two students, ensuring that each of them gets at least two books. In how many ways can she do this?"
I was thinking we can first choose 2 books p(10,2) and give them 1 each and then use the number of surjection formula to get S(8,2) on the remaining 8 books, and report the final answer as p(10,2)* S(8,2).
But I feel like it is very wrong. There are many repetitions in the answer.
Can you please help me understand how to correctly do the math, using the same logic of first giving them 1 book each.
Thanks
Formula used:
