HMMT November 2024 U26

A right rectangular prism of silly powder has dimensions $20 \times 24 \times 25$. Jerry the wizard applies 10 bouts of highdroxylation to the box, each of which increases one dimension of the silly powder by 1 and decreases a different dimension of the silly powder by 1 , with every possible choice of dimensions equally likely to be chosen and independent of all previous choices. Compute the expected volume of the silly powder after Jerry's routine.