statistical mechanics involving the multiplicity of a two state magnet final answers provided

Hi, I am looking for an explanation for part b and c of the attached work. I understand part a completely but am not understanding the process behind part b and c. Please provide a step by step solution to each part of the question that makes it easy to understand.

A free link to the course textbook can be found here (for reference the combinatorics of two-state paramagnets are covered in chapter 2): https://islamabad-institute.weebly.com/uploads/1/3…