How many ways can you pick 5 students from 27 students, ordered? (Meaning the ordering of the students matters.)

How many ways can you pick 5 students from 27 students, unordered? (Meaning the ordering of the students doesn’t matter.) To approach this, try to use the solution to the last problem, but adjust for overcounting. Hint: how many times did you count each solution?

Fix n and m in general (assume m is greater than or equal to n, both positive integers). How many ways can you pick n students from m students, unordered?

Think about the rest of the problems on your counting worksheet. We will discuss these in class, but get a head-start pondering them. Also, an apology that the worksheet does not involve any non-binary people (there are lots of girls/boys and women/men). I’ll have to add some more problems!

Finally, I would appreciate if you would include a copy of your self-evaluation sheet with this submission. Along with our first in-class test, I’d like to review participation in the class and this will help me see how people are doing. If you have any comments on your participation/comfort/success/feelings about the class, please feel free to include these. It will help me get a view of how things are going.