6.º a 8.º gradoDiscrete MathematicsPlanificado
Counting principles
The addition and multiplication principles, ordered arrangements (permutations), factorial notation and complementary counting.
math.discrete.counting-principles
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Se basa en
Requisitos previos obligatorios, hasta el fondo: 5
Aprenderás a
- Apply the addition and multiplication principles to count outcomes.
- Count arrangements of n objects (n!) and ordered selections of k objects from n.
- Use complementary counting, for example to count passwords containing at least one digit.
Definición
- n! = n × (n − 1) × ⋯ × 1 for n ≥ 1, and 0! = 1.
- A permutation is an ordered arrangement of objects.
Teorema
- Addition principle: if A and B are disjoint finite sets, |A ∪ B| = |A| + |B|.
- Multiplication principle: |A × B| = |A| · |B|.
- The number of ordered selections of k objects from n distinct objects is n!/(n − k)!.
Errores frecuentes
- Adding where the multiplication principle applies, or multiplying where the addition principle applies.
- Counting overlapping cases twice.
Conduce a
Descubrimientos opcionales
- Probability Counting equally likely outcomes gives probabilities.