Example
For example, if k = 5, n = 4, and a set of size n is {a, b, c, d}, then ★|★★★||★ would represent the multiset {a, b, b, b, d} or the 4-tuple (1,3,0,1). The representation of any multiset for this example would use 5 stars (k) and 3 bars (n − 1).
Seven indistinguishable one dollar coins are to be distributed among Amber, Ben and Curtis so that each of them receives at least one dollar. Thus the stars and bars apply with k = 7 and n = 3; hence there are ways to distribute the coins.
Read more about this topic: Stars And Bars (combinatorics)
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“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
—Marcel Proust (1871–1922)