Derren Brown and Lottery Magic

So, Derren Brown. Guessing lottery numbers. Correctly*. What's the probability of him getting everything right by blind luck?

Let's say Derren's less-talented brother, Gordon, also played the lotto on Wednesday and - by a sheer fluke - also guessed that 2, 11, 23, 28, 35 and 39 would be drawn.

What's probability of the first ball drawn being on Gordon's ticket?

There are six balls on the ticket, and 49 in the machine - Sapphire - they're using for the draw. The probability of any particular ball coming up is one out of 49, and we have six that would be good news - so the probability of the first ball being on the ticket is 6/49.

And the second ball?

Now we only have five balls left in the machine that we want to see. There is also one fewer ball in the machine, so the probability of Gordon liking the second ball is 5/48.

How about the rest of them?

The rest work the same way. Each time there is one fewer ball that helps us to win, so the top goes down by one; each time there is also one fewer ball in the machine, so the bottom goes down by one each time as well. The third ball would be 4/47, the fourth 3/46, the fifth 2/45 and the final ball 1/44.

Now what do we do with those?

We just multiply them all together. We get 720 / 10,068,347,520, which works out to be 1 / 13,983,816 - just a little better than the one in fourteen million you might have heard mentioned.

How do you know it was a trick?

Easy. Derren Brown is a magician. Also, if he knew the numbers before the draw, he'd have shown them before the draw. And probably bought a ticket.

* Of course it's a trick. The deep maths he's talking about? Nuh-uh.