LT

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.

Question qty: 10
Duration in minutes: 16
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Sample questions

  • How many different pairs can be chosen from n students? Order within a pair does not matter.
  • From n students, r distinct offices are assigned. How many assignments are possible?
  • There are a shirt choices and b trouser choices. How many outfits are possible?
  • When does order matter in a counting problem?
  • A code has r positions. Each has n symbol choices and repetition is allowed. How many codes?
  • In how many ways can n distinct students be arranged in a row?
  • When is the product rule used instead of the addition rule?
  • Choose one of a buses or one of b trains. How many choices are there?

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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