Permutations and combinations
A permutation counts the number of ways to arrange a set of items where order matters, while a combination counts the number of ways to choose items where order doesn't matter: arranging 3 books on a shelf out of 5 is a permutation (5 x 4 x 3 = 60 ways), while choosing 3 books to take on a trip out of 5 is a combination (60 / 6 = 10 ways, dividing the 60 arrangements by the 3! = 6 orderings of any 3 chosen books, since those 6 arrangements only differ by order). These counts feed directly into probability: if every outcome is equally likely, the probability of an event is the number of favorable outcomes, often counted with permutations or combinations, divided by the total number of possible outcomes.
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