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Combinatorics and probabilities
Combinatorics is the branch of mathematics concerned with the counting, arrangement, and organization of objects or elements into sets, especially when the exact details of each object are less important than the overall assessment of the structure or pattern.
Probabilities, on the other hand, relate to the likelihood or chance of events. It is a branch of mathematics that deals with the amount of uncertainty or probability. It involves calculations that estimate the probability of different outcomes under certain assumptions or conditions.
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Sample questions
- The die has 6 faces, of which 3 have an even number of points. Calculate the probability that the die will roll an even number of points.
- When buying a cheeseburger, you can choose between ___ different spreads and ___ different cheeses. How many different burgers can you choose?
- When buying a kebab, you can choose from ___ different types of meat, ___ different types of salad and ___ sauces. How many different kebabs can you choose?
- When making a sandwich, you can choose one of ___ different types of butter or one of ___ different spreads. How many different sandwich variations can you make?
- When making a sandwich, you can choose from ___ different types of butter, ___ types of cheese, ___ types of sausage. How many different sandwiches can you make if you like butter and cheese or butter and sausage?
Combinatorics and probability
Combinatorics provides systematic methods for counting possible choices. If a first item can be chosen in a ways and a second item in b ways, there are a × b independent pairs. Outcomes can also be organised in a table or tree diagram.
Probability
When outcomes are equally likely, the probability of an event is the number of favourable outcomes divided by the total number of outcomes. Probability ranges from 0 to 1: 0 represents an impossible event and 1 represents a certain event.
Do not omit possibilities or count the same outcome twice. If order is irrelevant, A–B and B–A may represent the same choice; if order matters, they are different outcomes.
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