Expected subgraph count in the Erdős-Rényi model
= Expected subgraph count in the Erdős-Rényi model
If a fixed graph $H$ has $v$ vertices, $e$ edges, and $N_H(n)$ unlabelled copies in $K_n$, then the number $X_H$ of its copies in $G(n,p)$ satisfies
$$
\mathbb E X_H=N_H(n)p^e.
$$
This follows by writing $X_H$ as a sum of <indicator random variables>.