Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 47 / 4 / b / Solution

Since the original observations are distinct, a bootstrap sample has no repeated value precisely when it contains all $n$ original values once. Of the $n^n$ equally likely ordered resamples, $n!$ are permutations without repetition. ThereforeThe probability is zero for $n=1$ and rapidly approaches one as $n$ grows.