91Ó°ÊÓ

In how many ways can you pass out \(k\) identical apples to \(n\) children if each child must get at least one apple?

(This problem is for students who are working on the relationship between \(k\)-element permutations and \(k\)-element subsets.) List in lexicographic order all three-element permutations of the five-element set \(\\{1,2,3,4,5\\}\). Underline those elements that correspond to the set \(\\{1,3,5\\}\). Draw a rectangle around those that correspond to the set \(\\{2,4,5\\}\). How many three-element permutations of \(\\{1,2,3,4,5\\}\) correspond to a given three- element set? How many three-element subsets does the set \(\\{1,2,3,4,5\\}\) have?