VG2
statistikk
Quiz
What is combinatorics?
Combinatorics is the mathematics of counting — how many ways can we choose or arrange elements?
Combinatorics is the mathematics of counting — how many ways can we choose, arrange or combine elements? It is the foundation of probability theory.
The multiplication principle
Number of possibilities = n₁ · n₂ · n₃ · ...
Permutations — order matters
P(n, k) = n! / (n-k)!
Example: How many ways can 3 of 5 students stand in a queue?
P(5, 3) = 5! / 2! = 60 ways
P(5, 3) = 5! / 2! = 60 ways
Combinations — order does NOT matter
C(n, k) = n! / (k! · (n-k)!)
Example: How many ways can we choose 3 of 5 students for a group?
C(5, 3) = 5! / (3! · 2!) = 10 ways
C(5, 3) = 5! / (3! · 2!) = 10 ways
Remember the difference:
Permutation: AB ≠ BA (order counts)
Combination: AB = BA (order does not count)
Permutation: AB ≠ BA (order counts)
Combination: AB = BA (order does not count)
Combinatorics is the art of counting without counting — seeing the pattern behind the numbers.
— Blaise Pascal (1623–1662)
🧠 Test yourself
Question 1 of 5
What is the difference between permutation and combination?
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