Please check my answers, if any of these is not correct, please help. Thank you very much.

Three marbles are drawn at random from an urn containing 8 black, 7 white, and 5 red marbles.

What is the probability that none of them are white. Answer: $\displaystyle \frac{_{13}C_3}{_{20}C_3}$.

What is the probability that at least one of them is red? Answer: $\displaystyle 1-\frac{_{15}C_3}{_{20}C_3}$

A drawer contains 8 blue socks, 4 green socks, and 6 brown socks. If you choose 2 socks at random, what is the probability that they are both brown? Answer: $\displaystyle \frac{_{6}C_2}{_{18}C_2}$

On a 10-questions true-false test, the questions are answered at random. What is the probability of answering at least 8 questions correctly? Answer: $\displaystyle .5^8+.5^9+.5^{10}$

Three letters are chosen at random from the word POSTER. What is the probability that the selection will contain E or O or both?

Please help me with this one.