  A graph $G$ is $H$-covered by some given graph $H$ if each vertex in $G$ is
contained in a copy of $H$. In this note, we give the maximum number of
independent sets of size $t\ge 3$ in $K_n$-covered graphs of size $N\ge n+t-1$
and determine its extremal graph. The result answers a question proposed by
Chakraborit and Loh. The proof uses an edge-switching operation of hypergraphs
which remains the number of independent sets nondecreasing.
