  Fix $k\ge 11$ and a rainbow $k$-clique $R$. We prove that the inducibility of
$R$ is $k!/(k^k-k)$. An extremal construction is a balanced recursive blow-up
of $R$. This answers a question posed by Huang, that is a generalization of an
old problem of Erd\H os and S\'os. It remains open to determine the minimum $k$
for which our result is true. More generally, we prove that there is an
absolute constant $C>0$ such that every $k$-vertex connected rainbow graph with
minimum degree at least $C\log k$ has inducibility $k!/(k^k-k)$.
