A spymaster has a network of 7 operatives whom he pays out of a slush fund containing $20000. For accounting reasons, his service requires him to use up his entire fund and to pay his operatives in integer multiples of $1000.
(a) How many different ways can he pay his operatives?
(b) Since an unpaid operative is unreliable, the spymaster decides that every operative will get at least $1000. With this rule, how many different ways can he pay his operatives?