Question: Five people have just won a $100 prize, and are deciding how to divide the $100 up between them. Assume that whole dollars are used, not cents. Also, for example, giving $50 to the first person and $10 to the second is di↵erent from vice versa.
(a) How many ways are there to divide up the $100, such that each gets at least $10?
(b) Assume that the $100 is randomly divided up, with all of the possible allocations counted in (a) equally likely. Find the expected amount of money that the first person receives.