(52!)/(13!)^4
Countless news stories have been published in the last 100 years about a perfect bridge hand being dealt. That is, a deck of cards being dealt to four people, and each of them ending up with a complete suit (see picture below). Here's a story from 1929. Here's one from 1935. Here's 1949. Here's 1954. Here's 1963. Here's 1978. Here's 1998. Here's 2011.
There's almost no chance any of these deals actually occurred. We can be almost certain that either (1) the stories were simply made up, or (2) the decks were not shuffled, but stacked.
We can deduce this for two reasons.
First, the raw math. The odds are 2,235,197,406,895,366,368,301,599,999 to 1 against such a deal happening. If the entire world played bridge nonstop 24/7, you'd expect such a deal to happen every 5 trillion years or so. It's not impossible, just absurdly unlikely.
Second, the fixation on the perfect deal. There's nothing special about the perfect deal that makes it less likely to happen than any other deal. In fact, it's the same 2,235,197,406,895,366,368,301,599,999 to 1 against any specific bridge deal from happening. You are just as likely to get the perfect deal as you are to get this one:
Of course, no one writes news stories about this hand because it doesn't appear special. To our eyes, it looks like every other regular hand you are dealt, where each player has a mix of suits and strong/weak cards. But make no mistake, the hand above almost certainly has never been dealt in the history of the world, either.
And while no one is going to write a newspaper article about this impossibly-unlikely deal, you might expect to find an article or two about other deals that do appeal to the human sense of wonder---like each player getting 12 cards of the same suit, King through deuce, plus the Ace of another suit. Or each player getting all the cards of one suit, except they have the Jack of the other suit of the same color.
You never hear about anything like that getting written up. And I'm reasonably sure, if those deals every actually happened, you would see them written up.
Instead, we just have dozens of write-ups of perfect deals. Why? Because people stacking decks stack perfect deals, not almost perfect-deals.