Test
Combinatorial rules
This test applies the addition and product rules of combinatorics. Students count possible selections and arrangements, organise a solution systematically and avoid including duplicate outcomes.
Time left: 00:00:00
Sample questions
- There are ___ shirt choices and ___ trouser choices. How many outfits are possible?
- Choose one of ___ buses or one of ___ trains. How many choices are there?
- In how many ways can ___ distinct students be arranged in a row?
- From ___ students, ___ distinct offices are assigned. How many assignments are possible?
- How many different pairs can be chosen from ___ students? Order within a pair does not matter.
Combinatorial rules
Use the addition rule for mutually exclusive alternatives and the multiplication rule for successive stages of a choice. The factorial n! counts arrangements of n distinct objects.
Order and repetition
If order matters, count arrangements; if it does not, count combinations. The number of combinations is C(n, k) = n!/[k!(n − k)!]. Before selecting a formula, decide whether objects are distinct, repetition is allowed and changing their order creates a new outcome.
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