I found a seemingly simple question in a popular book on probability:
A draw for a football cup is to be made. There are $n$ teams ($n$ of course being even). So there will be $n/2$ matches. You can bet on the pairings of the actual matches. You will get $p$ for each correct guess, e.g. if team $A$ plays against team $B$ and you guessed that you will get $p$.
The question is how much would you be prepared to offer for the right to make the $n/2$ guesses?
This doesn't seem to be as easy as I thought it to be. The reason for this is that on the one hand you will have binomial coefficients but there is another layer of complexity because you draw the matches without replacement so you have to deal with conditional probabilities and the last match will of course be fixed without further drawing. But perhaps I am missing something and there is an easy way out?
Is this a well known problem? Is it normally posed in a different form (e.g. cards)? When not answering directly perhaps you'll have some references for me.
P.S.: I slightly generalized the question in the book but I won't mention the title for the moment because the answer given there is not very well explained, so it doesn't add any value.