Solution
= 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. Therefore
$$
\boxed{P(\text{at least one repeated value})=1-\frac{n!}{n^n}.}
$$
The probability is zero for $n=1$ and rapidly approaches one as $n$ grows.