KöMaL 2020 A784

Let $n$, $s$, $t$ be positive integers and $0<\lambda<1$. A simple graph on $n$ vertices with at least $\lambda n^2$ edges is given. We say that $(x_1,\ldots,x_s,y_1,\ldots y_t)$ is a good insertion, if letters $x_i$ and $y_j$ denote not necessarily distinct vertices and every $x_iy_j$ is an edge of the graph ($1~\le i \le s$, $1\le j\le t$). Prove that the number of good insertions is at least $\lambda^{st}n^{s+t}$.