A teacher distributes 200 extra credit points to the students in her class of 20 students over the course of a month. Each child gets some number of points and the total number of points given to all the children is 200.
(a) How many ways are there for her to distribute the points?
(b) How many ways are there for her to distribute the points if each student gets at least five points?
(c) How many ways are there for her to distribute the points if each student gets the same number of points?
(d) How many ways are there for her to distribute the points if a particulat student, Amanda, gets no more than 10 points?