Math Question. PLEASE HELPPPP!!! Ill give 10 POINTS!

Some people believe in the force (yes, like in Star Wars). To test if young Anakin Skywalker has the force with him, he is told that some cards that Yoda can see but Anakin cannot contain a picture of a planet, a lightsaber, a laser rifle, or a spaceship. As Yoda looks at 20 such cards in turn, Anakin tries to guess what is on the card Yoda is looking at. Of course, Anakin has a 25% chance of simply guessing correctly.

a) Verify that the count of correct guesses in 20 cards follows a binomial distribution and write the notation.
b) What is the mean number of correct guesses?
c) What is the probability that Anakin guesses all 20 cards correctly?
d) Suppose Anakin guesses correctly on 10 of the cards. What is the probability of him doing this well or better by chance? Do you think he has the force with him?

if he knows the 20 cards are 5 each of the four options mentioned,
(assuming a 20-card deck and that those four are the only possibilities)
then after having seen all 5 "planets", for example,
he would know that there will be no more "planets";
so then he 'guesses' from only three choices...

if no spaceships have appeared after 15 cards,
[all five planets, lightsabers & laser rifles accounted for]
then he should 'guess' all those last five spaceships correctly, right?