1. ## Mathematics Conference

A two-day mathematics conference has n participants. Some of the participants give a talk on Saturday, some others give a talk on Sunday. Nobody gives more than one talk, and there may be some people who do not give a talk at all. At the end of the conference, a few talks are selected to be included in a book. In how many different ways is this all possible if we assume that there is at least one talk selected for inclusion in the book?

2. ## Re: Mathematics Conference

Originally Posted by alexmahone
A two-day mathematics conference has n participants. Some of the participants give a talk on Saturday, some others give a talk on Sunday. Nobody gives more than one talk, and there may be some people who do not give a talk at all. At the end of the conference, a few talks are selected to be included in a book. In how many different ways is this all possible if we assume that there is at least one talk selected for inclusion in the book?
What the heck do Saturday or Sunday have to do with the answer?

If there are $\displaystyle K,~1\le K\le n$ papers given then there are $\displaystyle 2^K-1$ subsets of papers.

3. ## Re: Mathematics Conference

Originally Posted by Plato
What the heck does Saturday or Sunday have to do with the answer?
I suppose that if A gives a talk on Saturday that is selected for the book, it is considered a different possibility than if A gives a talk on Sunday that is selected for the book.
So for n = 1, we would have 2 possibilities.

For n=2,
A speaks on Saturday (1 possibility)
B speaks on Saturday (1 possibility)
A speaks on Sunday (1 possibility)
B speaks on Sunday (1 possibility)
A and B speak on Saturday (3 possibilities)
A and B speak on Sunday (3 possibilities)
A speaks on Saturday and B speaks on Sunday (3 possibilities)
B speaks on Saturday and A speaks on Saturday (3 possibilities)
In all, there are 16 possibilities.

So, we need to find the number of possibilities as a function of n.

4. ## Re: Mathematics Conference

Originally Posted by alexmahone
In how many different ways is this all possible if we assume that there is at least one talk selected for inclusion in the book?
Look carefully at that question.
Whether a talk is given on Sat. or Sun. does not change its print version, does it?

5. ## Re: Mathematics Conference

Originally Posted by Plato
Whether a talk is given on Sat. or Sun. does not change its print version, does it?
It would, if the print version of a talk begins: "This talk was given by Mr X on _____day."

I cannot see any other reason the author (Miklos Bona) chose to include 'Saturday and 'Sunday' in this problem.

6. ## Re: Mathematics Conference

Originally Posted by alexmahone
It would, if the print version of a talk begins: "This talk was given by Mr X on _____day."

I cannot see any other reason the author (Miklos Bona) chose to include 'Saturday and 'Sunday' in this problem.
Misdirection

CB