If we have n ways to do one thing and k to do another, then there areĀ ānĆkāĀ ways to do BOTH (first thing AND the second thing), andĀ ān+kāĀ ways to do one thing OR the other thing.
In any scenario where we can putĀ ākāĀ items into each ofĀ ānāĀ positions, we haveĀ āknāĀ possible arrangements.
The number of different orders in whichĀ ānāĀ items can be arranged is
where each box is a "slot" in the order. In the first slot we can put any ofĀ ānāĀ items, in the second any of theĀ ānā1āĀ remaining items, and so on. We then multiply all of these together to getĀ ān!ā
The number of permutations, defined as an ordered arrangement, ofĀ ārāĀ items from a set ofĀ ānāĀ items can be calculated by:
Combinations are selections of items where order does not matter. For combinations ofĀ ārāĀ items from a set ofĀ ān:
which is the binomial coefficient.
Nice work completing Counting, here's a quick recap of what we covered:
Exercises checked off
IB exams will never ask you to
Beyond the syllabus, it can also help to: