math / Discrete Mathematics / free
Combinatorics
Count structured possibilities without listing every case.
Follow the mechanism1 / 3
A choice creates positions or a group. Before counting, identify whether the selected objects fill named roles or simply form a set of members.
counting choices6 items · choose 3
Focus the idea
Does order matter?
slot 16choices
slot 25choices
slot 34choices
×ordered count1206P3
same selected itemsA · B · C
reordered viewB · A · C
A · B · C and B · A · C are different assignments because the positions carry meaning.
available items6
items chosen3
ways120
orderings per group6
6 choices fill the first slot, then 5, and so on. Because positions matter, there are 120 ordered outcomes.
Combinatorics is the art of counting without listing. First ask whether order, repetition, or both matter; then choose a counting rule that matches the structure of the choice.