That defines the permutation.

What's going on here is that this random permutation combined with the permutation of the prisoner's names in the boxes gives you a permutation of the prisoners, which is a uniformly random permutation.

But the permutation is defined in the following way.

That means that in the permutation, A goes to G.

It's to compute the probability that a random permutation contains a long cycle.

You also have to come up with is permutation, this is also something you have to define.

Why would this be better than just going through in their permutation order or something like that?

Now, it turns out that it's actually very easy to compute the probability that a permutation contains a long cycle.

And people always give you the same permutation of the same three things under capitalized, the wrong people, bad market conditions.

We'll generate a new list Lâ and we're going to put in that list what's going to be a permutation of these values.

So now we're going to take this mortgage backed security and introduce one step further kind of permutation or derivative of what this is.

Helper functions like is sorted or is permutation will probably be helpful later in the future because you may be able to reuse them for other purpose.

Why did your product or why did your company fail? and people always give you the same permutation of the same three things under capitalized, the wrong people, bad market conditions.

So, the probability that our permutation contains a cycle of length greater than 50 is 1 51 1 52 1 53 ... 1 100, which is about n log 2 0.69 something.

First, we assume that the list y that we will return actually is sorted, but we also need to make sure that the list we returned is a permutation of our input list.

It's just a little just write down the binomial coefficients that the probability that the permutation contains a cycle of length k where k is bigger than n 2 is exactly 1 k.

And up here, the way we would write this permutation, we would say, well, how many ways can we fit 7 people into 3 chairs if we care about what chair they're sitting in?

In other words, they choose a random permutation of the boxes and assign ownership of the boxes, and every prisoner gets to know all the ownerships, gets to memorize all the ownerships and everything.

So, what's going to happen is that prisoner A will find his own name if in this permutation the cycle that his name is in, the cycle that A is in has length at most 50.

A lot of people, they learn the permutation notation and they say, oh, that's n factorial over n minus k factorial, where n is the number of things I need to place and n minus the whole thing factorial.

That every person here, every decision that you've made today, every decision you've made in your life, you've not really made that decision, but in fact, every single permutation of those decisions is made, each one going off into a new universe.