Set: 1. No ordering
2.Countable 3. No repetition
Set Coefficient: (n,k)=n(n-1)…(n-k+1)/k!
Interpretation 1: the no. of subsets of cardinality of k of a set of cardinality of n, i.e. choose k items from n distinct items without repetetion (combination).
Interpretation2: the no. of positive roots for equation X0+...Xk=n+1
Multiset: 1. No ordering 2.Countable
Multiset Coefficient: ((n,k))=n(n+1)…(n+k-1)/k!=(n+k-1,k)
Interpretation 1: the no. of sub multisets of cardinality of k of a set of cardinality of n, i.e. choose k items from n distinct items with repetetion (combination with repetition).
Interpretation 2: the no. of non-negative roots for equation X0+...Xk=n+1