Question 4 Mathematical induction (8 points) Please prove that 13 + 23 + - - - + n3 : \"2(n4+1)2 where n is an arbitrary positive integer. Question 5 Counting (13 points) 1. Please answer the following questions. (a) How many functions are there from a set with three elements to a set with eight elements? (b) How many one-toone functions are there from a set with three elements to a set with eight elements? 2. What is the coefcient of 3:73;\" in (23; $)19