this is question 13 from algorithms 4th edition chapter 2.2. can anyone help me solve it? it is not solved in the solution manual

Lower bound for average case. Prove that the expected number of compares used by any compare-based sorting algorithm must be at least ~N lg N (assuming that all possible orderings of the input are equally likely). Hint.The expected number of compares is at least the external path length of the compare tree (the sum of the lengths of the paths from the root to all leaves), which is minimized when it is balanced.

here is the url

http://www.chegg.com/homework-help/Algorithms-4th-edition-chapter-2.2-problem-13E-solution-9780321573513

thanks in advance :)