1. The problem statement, all variables and given/known data A teaching event takes two days and involves n people. Some of the people give a talk on day 1, some others give a talk on day 2. Everybody gives at most 1 talk, and there can be some teachers who do not give a talk in either of the two days. At the end of the event, a few talks are picked to be included in a book. In how many different ways can this all happen? (there has to be at least one talk selected) 2. Relevant equations 3. The attempt at a solution I suspect that once you have found in how many ways can you have people give talks in either of the two days (say x), you can use that a set containing x elements has 2^(x) subsets and this would be the number of possible ways to select the talks.