Why did God let Adam sin?
God allowed Adam to sin because, in His sovereign workings, mankind was to be left with a real alternative. Without that choice, there would be no exercise of the will; the human race would have been like robots. As created beings, people are given the capacity to accept or reject God's offer of salvation.
Les explains that it was in the sovereign workings of God that man should be left with that alternative. Otherwise there would be no choice and no exercise of the will. If Satan had not been permitted to come into the garden, and if sin had not entered, the human race would have been without choice, like robots. But humans are not robots; they are created beings given a choice to reject or accept God's tremendous offer of salvation. This connects to the fall of Adam and the universal sin problem: death passed upon all men, and all have sinned because it started with Adam.