email@example.com says... > Don McDonald <firstname.lastname@example.org> wrote:
[Mean lowest number in a 40-choose-6 lotto game]
> > > = 41/7 > > > > =?? (N+1) / (L+1). ?? > > is this correct.? [snip] > > possible argument about beads on a necklace. > Yes, how does it go again?
Isn't it something like this:
The N numbers represent gaps between N+1 beads on a string. Choosing L numbers from N without replacement corresponds one-to-one to choosing a way of colouring the N+1 beads with L+1 colours, with at least one bead of each colour (since without replacement), and then stringing them on the string so that colours are contiguous and in a particular order. (The gap between two beads of different colours represents a lotto number.) The mean value of the lowest number equals the mean number of beads of the first colour (or any colour), and that's easy to work out.