Si osserva che le permutazioni sono casi particolari delle disposizioni semplici: le permutazioni di un insieme di n oggetti sono le disposizioni semplici di tali oggetti di classe n. In effetti per il loro numero: Disposizioni con ripetizioni Consideriamo un insieme costituito n - elementi distinti ed un numero naturale k senza alcuna limitazione superiore. Combinazioni con ripetizioni si possono prendere in considerazione anche le combinazioni con ripetizione. Ad esempio, vi sono modi di distribuire a 2 bambini distinguibili 4 caramelle indistinguibili, contando anche i casi in cui uno dei bambini non riceve nessuna caramella: , , , , Oppure, le combinazioni con ripetizioni per n oggetti di classe k rappresentano il numero delle derivate parziali di ordine k calcolabili per una funzione a n variabili.

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Per quanto riguarda le cifre, esse sono raggruppamenti di elementi, scelti da un insieme che ne contiene. A fine serata si salutano e ognuno stringe la mano a tutti gli altri. Quante strette di mano ci saranno? Ovviamente e in quanto una stretta di mano avviene fra due persone. NO, sarebbe assurdo infatti che ciascun tipo salutasse se stesso stringendosi da solo la mano.. Per contare il numero delle strette di mano ricorreremo quindi alle combinazioni semplici, da cui: 3 8 amici si incontrano settimanalmente per un banchetto, cambiando ogni volta la loro posizione lungo una tavolata.

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