Disposal refers to the act of getting rid of something by throwing away, giving away, burning, or assigning: "The problem of waste disposal in this village is acute." "What disposal will you make of these old clothes?" Disposition also conveys the idea of placing, arranging, and ordering, but only when such acts are performed according to a plan: "The general ordered a strategic disposition of his troops." "The deceased man's will arranged for the disposition of his property." Think of disposal as "disposing of," of disposition as "disposing."
Dictionary of problem words and expressions. Harry Shaw. 1975.