Fixed solution to 1.11

Update 5.tex

Fix incorrect solution to Chapter 1 Mixed Problem 57 by adding the combinatorial part for Principle of Inclusion-Exclusion

add solution to problem 5.43

Update 12.tex

Update 12.tex

Create 12.tex

Update index.tex

Update index.tex

Fix solution to problem 5.1

minor fix to the solution of problem 5.51

Rename src/chapters/6/sections/moment_generating_functions/15.tex to src/chapters/6/sections/moment_generating_functions/problems/15.tex

Create 15.tex

Create index.tex

Update index.tex