Question 160
$n$ countries send delegates to an international Festival, each country send $k$ delegates ($n$ and $k$ are integers satisfying $n \gt k \gt 1$). The organizing committee of the Festival divides $nk$ delegates into $n$ discussion groups, each group consists of $k$ delegates. Show that one can choose $n$ delegates, in such a way that each group has one delegate be selected and each country has one delegate be selected.