Use tilde notation to simplify each of the following formulas, and give the order of growth of each:

a. \(n(n-1)(n-2)(n-3) / 24\)

b. \((n-2)(\lg n-2)(\lg n+2)\)

c. \(n(n+1)-n^{2}\)

d. \(n(n+1) / 2+n \lg n\)

e. \(\ln ((n-1)(n-2)(n-3))^{2}\)