  Atom-number states are a valuable resource for ultracold chemistry, atom
interferometry and quantum information processing. Recent experiments have
achieved their deterministic preparation in trapped few-fermion systems. We
analyze the tunneling decay of these states, both in terms of the survival
probability, and the non-escape probability, which can be extracted from
measurements of the full counting statistics. At short times, the survival
probability exhibits deviations from the exponential law. The decay is governed
by the multi-particle Zeno time which exhibits a signature of quantum
statistics and contact interactions. The subsequent exponential regime governs
most of the dynamics, and we provide accurate analytical expressions for the
associated decay rates. Both dynamical regimes are illustrated in a realistic
model. Finally, a global picture of multi-particle quantum decay is presented.
