Wordwhirled (Part 1)

My kids have taken to watching a show called WordWorld.  It’s pleasant, educational, and in some ways, scary.  The basic premise of the show is that the word which represents something is the thing it represents.  A duck, for instance, would be made of the letters D-U-C-K artfully rendered to look like a duck.  Similarly, a house would be the letters H-O-U-S-E sketched out to look like a mansion.

Characters in the show have the ability to take a group of letters and press them together for the express purpose of making what they need.  If they are in need of a nice, new carpet, they would go into the pool of letters in their home, take out R, U, and G, and smoosh them together until they formed RUG.  The letters would amalgamate into their new configuration, and no more cold feet.

It concerned me, though, that some of the characters seem functionally illiterate.  This is the plot of some episodes, in fact.  A character, usually duck, will accidentally forget a letter or remove a letter and end up with the wrong thing.  Hilarity ensues.  Hilarity, that is, until he accidentally makes something truly dangerous.

This possibility has not been explored in the show, to the best of my knowledge.  I assume there is some mechanism which protects the inhabitants from their pools of letters creating BOMB or NUKE.  Those words are so small, though, that the chance of them happening by accident is fairly large compared to the chance of something like WEAPON or CATACLYSM.

Out of a pool of 26 letters, the chance that it would create an arbitrary grouping of 4 particular letters is [math]26^4 = 456976[/math] .  Surprisingly large.  How likely is a seriously damaging combination in practice?  I decided to find out, in part two.

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