A quick quiz consists of 5 multiple choice problems, each of which has 4 answers, only one of which is correct. If you make random guesses on all 5 problems

(a) What is the probability that all 5 of your answers are incorrect?
(b) What is the probability that all 5 of your answers are correct?

Here's a rule of thumb that works for these probability questions.
Let say there are 5 objects and you can 3 of them. Then the total number of ways are:
5x4x3=60
This is because at the beginning there are 5 objects to choose from, after one is chosen, there's only 4 left. After another one is chosen, there is only 3 left. That's when you are done with your 3 turns to choose.
I am a bit busy and I will tell you later