Counting carefully, and knowing when not to count at all.
Combinatorics is about counting without listing. The hard part is rarely the arithmetic; it is finding the description of the set that makes it countable in the first place.
Expect arrangements and selections, the pigeonhole principle, inclusion–exclusion, recursions, and bijections. A surprising number of these are solved by counting the same thing twice and setting the two answers equal.
Browse every Combinatorics problem →