I do not use R but I think the problem is in the function dbinom(). I have a feeling that the first parameter of 1,100,000 is in correct. I would think the first variable would be the amount of times you expect the word 'the' to appear.

In other words given the word 'the' has a probabilty of 0.06 then the chance it will occur 11,100,000 times given 18,600,000 words appear is 0.04

this first parameter can very for finding the probabilty of X amount of 'the' depending on how many you desire.

Here is the main problem, if you looked at the binomial theorem this would all make much more sense.