Create “self-created” questions for each of the Combinatorics (discrete math) topic

Create “self-created” questions for each of the Combinatorics (discrete math) topic, and also create solutions for the questions:
(no textbook questions allowed)
1) The pigeonhole principle
2) Binomial identities (Combinatorial proofs)
3) Partitions (Compositions, Set Partitions, and Integer Partitions)
5) The Inclusion-Exclusion method
6)Generating functions (Modelling using them& Using them to find a closed form for recurrence relations)
7)Graphs
8) Trees