Exercise 11.4.1: Building a generating function for selecting subsets from a heterogeneous set. About (a) Give a generating function denoting the number of ways to select a subset from a set of three identical apples. (b) Give a generating function denoting the number of ways to select a subset from a set of bananas. There are a total of four bananas, but they are bundled into two groups of two. (c) Now pool the apples and bananas. Give the generating function for the number of ways to select a subset from the pooled set.

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the major difference between the two is the objective and the reward of the game. candy crush has a puzzle theme with the objective of meeting a specific quota of points or objects, you are able to gain access to the next level and compete with peers on the process. on duolingo the objective is rather different, you are given sets of questions for you to answer for you to move to the next level and as for the reward, you are able to learn available language as this is an app developed to teach the user about other languages.