I'm gonna be honest, I don't think this is possible. Because you would need to find the exact amount of 4 letter words in the english laguage and all of its subsequent dialects. But I'm gonna make a try at it.
1334670722541009 is how many actual 4 letter word strings that can be made
87880 is all the possible words you are able to make, with at least 1 vowel in every word.
So
87880/1334670722541009 = 0.000000000065844
So you have about a 0.0000000065844% chance of getting an actual word.