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
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