A committee of two is selected at random from a set consisting of three Democrats, four Republicans, and one Independent.
What is the probability that the committee consists of no Republicans?
What is the probability that the committee consists of all Republicans?
The chance of picking a Republican as the first member would be 4 in 8 (= 0.5). The chance of picking a second would be 3 in 7 (= 0.43). So the chance of getting two together is 0.5 * 0.43 = 0.22. It's that easy.
If you don't understand this stuff, you should ask your teacher for clarification. They won't bite your head off. They are paid to teach you and they'd like nothing better than for you to learn it.