Answer:
e = 2.718
Step-by-step explanation:
- There're "n!" ways of arranging "n" numbers, supposing that there're n picks, then the first (n−1) picks are in descending order, there are (n−1) ways of choosing the first (n−1) numbers and thus the probability of picking just n numbers is:
                   (n-1) / n!
- The expected value (E) would be:
          E = ∑ n*(n-1)/n!
           = ∑ n*(n-1)/n*(n-1)*(n-2)!
           = ∑ (n = 2 to infinity) [ 1 / (n-2)! ] = ∑ (n = 0 to infinity) [ 1 / (n)! ]
           = e  ...... (Maclaurin series approximation)
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