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Question: each of the following combinatorial quantities are functions of a...

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Each of the following combinatorial quantities are functions of a positive integer n.

Let a(n) denote the number of possible pairs of people in an n person class.

Let b(n) denote the number of comparisons needed to determine whether if a specific integer is in a sorted list.

Let c(n) denote the number of n-digit positive integers.

Let d(n) denote the number of possible ways to rank n contestants in a race with no ties.

List the functions in increasing order by their asymptotic growth rates. In other words, list the functions as f1(n),f2(n),f3(n),f4(n), where for i=1,2 and 3, we have that fi(n)=O(fi+1(n)).

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