Let's find the opposite outcome: what's the probability that no vowels are chosen?
Well, BREAKDOWN has 9 letters, and 6 are consonants. The probability that the first letter chosen being a consonant is
Now assume we choose a second letter. We have left only 8 letters now, and since we already chose a consonant, only 5 consonants are left. The probability of picking a second consonant is
Using the same logic, the probability of choosing a third consonant is
So, the probability of choosing all 4 letters that are all consonants is:
What we want, however, is the case where at least
Thus, the probability we are looking for is: