(Solved): Assignment details: 1. Use the generating functions to model and find the solution for the followin ...

Assignment details: 1. Use the generating functions to model and find the solution for the following problem: In how many ways can we distribute 15 candies among 4 children, if each one should take at least 2 , the youngest child should not have more than 7 and the oldest one should take an even number? Resolve the equation. 2. Assume the relation $$R$$ over the set $$\{0,1,2,3,4,5,6,7,8,9\}$$ where $$(a,b)?R$$ if and only if $$a+b<10$$ : a. Determine if the relation is Reflexive, symmetric, antisymmetric, or transitive (Use a table). b. Represent your relation $$R$$ by a graph, and specify what type of graph can be used to represent this relation. c. Determine the degree of each vertex and the total degrees of the graph (Use a table). d. Generate an adjacency matrix for your graph.