New Problem: The Rockettes Return

Recall a previous problem (and its solution) about a line of dancers who come out on stage in a random order.

Now the question is: when they come out on stage in random order, on average, how many of them are already in the correct spot? (If necessary, give this as a function of $n$, the number of dancers).

It's pretty obvious who doesn't belong. (No, that's not a racist joke.)

4 Responses to “New Problem: The Rockettes Return”

1. New Problem: King of the Jungle Plays Tug of War « Arcsecond Says:

[…] Plays Tug of War By meichenl I have a couple of old problems I haven’t solved yet (1 2), but they’re kind of long, and this one is much shorter. The logic for this puzzle is from […]

2. Nik Says:

On average, less than one? I can’t think of a way to write it as function.

3. meichenl Says:

Not quite…

Think first about how to count the number of ways for them all to be in the wrong order.

4. Answer: The Rockettes Return « Arcsecond Says:

[…] Answer: The Rockettes Return By Mark Eichenlaub Six months ago I asked a question about the rockettes. […]