Short lists are often used in math camps to cover some subject by going through a bunch of problems. I've thought of doing the same for programming contests. The first list is related to combinatorics.

Discuss the solutions in the comment section.

Feel free to discuss the solutions in the comment section.

# (10th grade math course) How many different strings of length 9 are there which contain 3 'a's, 3 'b's and 3 'c's.
# How many ways are there to climb a n level stair if at each step you can climb one or two levels.