Advanced Complex Variable Math problem set -- 2

I have a problem worksheet for these type of complex variable question. Need a step by step solution. 1)Enumeration (elementary methods, inclusion and exclusion, Pigeonhole and addition principle, Euler’s function; Functions, words and selections; ordered selections without repetitions; permutations; power series and properties; Partial fractions; binomial theorem for negative exponents, etc); 2)Generating functions and applications (recurrence relations, partitions of positive integers, partitions and diagrams; conjugate partitions; Partitions and generating functions; restricted partitions, etc) 3)Graph theory and algorithms (connectivity, planarity, Hamiltonian cycle and Eulerian walk, Graphs; isomorphism; valency; paths and cycles; trees; vertex colouring, Planar graphs; Euler’s theorem etc); 4) Error correcting codes(Linear codes, construction and error correction, symmetry and counting)