# Question #e7870

##### 1 Answer

#### Explanation:

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:

#6/9(5/8)(4/7)(3/6)#

Simplifying...

#=2/3(5/8)(4/7)(1/2)=5/42#

What we want, however, is the case where at least

Thus, the probability we are looking for is:

#1-5/42=37/42#