  We find conditions required to achieve complete population transfer, via
coherent population trapping, from an initial state to a designated final state
at a designated time in a degenerate $n$-state atom, where transitions are
caused by an external interaction. In systems with degenerate states there is
no time ordering. Analytic expressions have been found for transition
probabilities in a degenerate $n$-state atom interacting with a strong external
field that gives a common time dependence to all of the transition matrix
elements. Except for solving a simple $n^{th}$ order equation to determine
eigenvalues of dressed states, the method is entirely analytic. These
expressions may be used to control electron populations in degenerate $n$-state
atoms. Examples are given for $n=2$ and $n=3$.
