【Disposal】 , 【disposition】 are frequently used without clear distinction when they mean the act or the power of disposing of something.

However, when the emphasis is upon what shall be done with money, property, or possessions,  【disposal】 tends to imply a getting rid of (as by selling, giving away, assigning to others, or destroying) and 【disposition】 ,a proper or orderly distribution or utilization.

When the idea of arrangement or ordering or of making arrangements is stressed, 【disposition】 , rather than 【disposal】 , is the more accurate term.

The idiomatic phrases at one′s 【disposal】 and at (or in) one′s  【disposition】 differ in that, though both imply a placing under one′s control, the former suggests use as one sees fit and the latter, subjection to one′s direction, arrangement, or command.