8 of the 11 bits represented by the last word are a checksum. 3 bits are part of the seed. That means that nominally, only eight words from the dictionary would complete a full set of 24. That's actually true in any position if you know where the word is missing. The complexity of the checksum though requires a program to find the eight possible words. (I think someone hereabouts wrote a script to do exactly that...)

This means you only have to try eight word sets in the Ledger. If you don't know the position of the missing word (but know that the other 23 are otherwise in the correct order), then you'll have to try 24*8 = 192 sets.