EXERCISE 12.4.3: Generating functions for selecting sets from different varieties. Let {fk} be the sequence corresponding to the number of ways to select a subset of k items from a se' 8. Give the generating function for {fk} for each description of S. (a) An infinite supply of identical items. An innite supply of items. There are two varieties of items. Items of the same variety are idenncal (b) (c) Six identical items. (d) Items come bundled in groups of three. There is an infinite supply and all items are the same. (e) There are 6 groups of items. Each group has 3 items. The items within a group are identical. Items from different groups are different. (f) There are two of each variety of item. The number of varieties is 20. (9) There are 20 distinct items