A standard 52 card deck is being used in an exciting experiment! A card is drawn randomly from the deck, its information is recorded, then the card is returned to the deck and it is thoroughly shuffled.

(a) Determine the probability that if we perform this process 6 times, we get exactly 3 diamonds, and exactly 1 spade.

(b) If we repeat this experiment 11 times, what is the probability that we get three times as many clubs as hearts.

(c) Determine the probability that if this process is repeated 5 times, there will be exactly 2 diamonds drawn, and at most 1 jack.

(d) Suppose we repeat this experiment 7 times. Determine the probability that we draw exactly 3 clubs and exactly 1 heart, if we know that we drew exactly 2 red cards.