With a pack of 52 playing cards (you can leave power and factorial in your answer):

a) If we draw a card from the pack, how many basic events are there?

b) If we draw two cards at once from the pack, how many basic events are there?

c) What is the maximum number of cards we need to draw without replacement to get a non-heart card?

d) What is the probability of drawing 12 cards at once and they are all of the same color?

e) What's the probability of the union and intersection of events (A): draw 5 cards one by one without replacement and at least 3 of them are heart; (B) draw 5 cards one by one without replacement and we used 3 draws to get the first heart card.