1) There are seventeen students in our class. Suppose I decide to send a group of you down to the computer room while the rest of us stay here in 204. I could send a pair of you, or three of you, or ten of you, etc.. And the pair could be any two of you-maybe Alex and Maia, or Sophia and Marisa, and so forth. It could even be just one of you, or all of you or none of you!
When you think about it, there are a LOT of different ways that the computer room delegation could be configured. Allow for any possible size of group, and any possible combination of people within the group. Count all the different possibilities.
STRATEGY NOTE: This is a hard problem, and you may have difficulty answering it immediately. To get a handle on it, you might want to start by assuming the class is much smaller (say four students total) and see how that works out first. Then increase the class size to five total students, and see what impact the increase has on the number of possibilities.
2) If you figure out a formula for counting the possibilities for any size class, develop a justification for the formula. If it involves powers, factorials, or whatever, say why it should have those operations. An explicit formula does exist, by the way.
3) Once you know how many different ways I could pick the group, determine the probability that the group will include you (specifically you, the person reading this sheet).
4) Next determine the probability that the group will be composed entirely of boys.
5) Why do you suppose this worksheet is named "Set of All Subsets"?