Comparison between Sets&Multiset(Bag)

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