Combinatorics
n and k → permutations P(n), arrangements A(n,k), combinations C(n,k)
Parameters
P(n) = n! — ordering all elements (arrange n books). A(n,k) = n!/(n−k)! — order matters, subset (gold/silver/bronze medals among n people). C(n,k) = n!/(k!(n−k)!) — order doesn't matter (committee of k from n). With repetition: nᵏ and C(n+k−1, k).
Results
- P(n) = n!
- 3 628 800
- A(n,k) = n!/(n−k)!
- 720
- C(n,k)
- 120
- nᵏ (with repetition)
- 1 000
- C(n+k−1,k)
- 220