  Let H = (V,E) be a k-uniform hypergraph with a vertex set V and an edge set
E. Let V_p be constructed by taking every vertex in V independently with
probability p. Let X be the number of edges in E that are contained in V_p. We
give a condition that guarantees the concentration of X within a small interval
around its mean. The applicability of this result is demonstrated by deriving
new sub-Gaussian tails for the number of copies of small complete and complete
bipartite graphs in the binomial random graph, extending results of Ruci\'nski
and Vu.
