To ordain means to order or decree (see decrees of God). It can mean to cause something to happen or to allow it to occur depending on the context. God can ordain things to occur without directly causing them.
God ordained The Fall in that he gave freedom of choice to the devil, Adam, and Eve. Each made a choice that was consistent with their natures. Adam freely chose to disobey God, but God did not cause Adam to disobey. Rather, the circumstances of Adam's free will, Satan's falleness, The Garden location, etc., were all in place and Adam freely chose to sin -- yet God did not cause Adam to sin.
Ordain is also used to mean to recognize and establish an individual to a specific office and/or calling. Ministers are ordained to their offices by the laying on of hands (1 Tim. 4:14) and are thereby charged with the duties of that office.