In a multiple-choice exam, there are 20 questions and each question has 3 choices. Say someone is totally unprepared and randomly chooses answers. Let Y be the number of questions he/she guesses...

In a multiple-choice exam, there are 20 questions and each question
has 3 choices. Say someone is totally unprepared and randomly chooses answers. Let Y be the number of questions he/she guesses correctly.
(a) What is the distribution of Y ? (its name and parameters are expected)
(b) Find P(Y = 6).
(c) Find P(Y ≤ 6).
(d) Find P(Y > 6).
(For questions (b), (c), (d), please write down the formulae for computation,
and R commands; first. Then, provide the numerical answers from your R
or RStudio outputs).