Answer:
e = 2.718
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)