We have 20 thousand dollars that must be invested among 4 possible opportunities. each investment must be integral in units of 1 thousand dollars, and there are minimal investments that need to be made if one is to invest in these opportunities. the minimal investments are 2, 2, 3, and 4 thousand
dollars. how many different investment strategies are available if:

(a) an investment must be made in each opportunity?
(b) investments must be made in at least 3 of the 4 opportunities?