<s>[INST] From a set of $n$ distinct positive integers, we choose $k$ integers, where $1\leq k\leq n.$ Calculate the probability $p$ that at least two of the integers have the same remainder when divided by $k.$ When $k\geq n,$ this probability is zero, since each integer in the set will be congruent to a different residue class mod $k.$ So we suppose $k[/INST]