Ellen must take 4 courses this semester. She has a list of 4 math courses and 6 science courses to from which to choose.
(a) Initially Ellen is under the impression that she can simply take any four of the courses on the list. If this was the case, how many different ways could Ellen select the four courses?
(b) Ellen's boyfriend tells her that he thinks that she must choose 2 math courses and 2 science courses to meet her degree requirements. If this is true, how many different ways can she select the four courses?
(c) Ellen's speaks to her advisor and finds out that her program actually only requires that at least one of her four courses be a math course. Knowing this, how many different ways can she select the four courses?