Four letters are picked from the word BREAKDOWN. What is the probability that there is at least one vowel among the letters?

Question

I know that the right answer is 0.881 but i'm not sure how to get there.

Answer 1

In the easy-to-verify form: $$ 1-\frac{\binom{6}{4}\cdot\binom{3}{0}}{\binom{9}{4}} $$

Answer 2

Use the complement rule. $P(\text{at lest one vowel}) = 1 - P(\text{no vowels})$. You have 6 non-vowels and 3 vowels. What can you do with this? The easiest thing to do is to draw a probability tree.