Using permutations & combinations alongside principles to count the ways things can be selected or arranged.
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Practice exam-style counting problems
If we have n ways to do one thing and k to do another, then there are ​n×k​ ways to do BOTH (first thing AND the second thing), and ​n+k​ ways to do one thing OR the other thing.
In any scenario where we can put ​k​ items into each of ​n​ positions, we have ​kn​ possible arrangements.
The number of different orders in which ​n​ items can be arranged is
where each box is a "slot" in the order. In the first slot we can put any of ​n​ items, in the second any of the ​n−1​ remaining items, and so on. We then multiply all of these together to get ​n!​
The number of permutations, defined as an ordered arrangement, of ​r​ items from a set of ​n​ items can be calculated by:
Combinations are arrangements of items where order does not matter. For combinations of ​r​ items from a set of ​n:
which is the binomial coefficient.