Of Sets and Sums

Probability Level 3

Consider the set $\lbrace{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\rbrace}$ .

For each of its subsets, let $M$ be the greatest number. Find the last three digits of the sum of all the $M$ 's.

Assume that $0$ is the greatest number of the empty subset.