A school gives 7 courses during a period of 6 months. These courses are all 1 month courses. If you are going to read 4 of these courses, in how many ways are there to do this? (Note that the order in which the courses are taken in is not nonessential and you can not read two courses at the same time).
Okay, since order here is a factor: the first time we should have 7 choices, the second 6, third time 5 and for the last course we should have 4 choices. Doesn't this mean that there are $\dfrac{7!}{3!}$ ways of doing this? I don't understand where the 6 months come in, does it matter, we are only taking 4 out of the classes.
We cannot read two courses in the same month, so we have to choose four months out of 6 to read the courses in – the 6 months come in here. There are $\binom64$ ways to do this. Multiply that by the $\frac{7!}{3!}$ ways to choose and order the courses, which you have calculated, and there are 12600 ways to pick/read courses for the semester.