(Solved): ( 6 points) Consider a deck of 52 standard playing cards which contains cards of 13 different values ...

( 6 points) Consider a deck of 52 standard playing cards which contains cards of 13 different values (Ace, 2, 3, ..10, Jack, Queen, King) in 4 different suits (shapes). The suits clubs and spades are black while hearts and diamonds are red. The deck is thoroughly shuffled and spread face-up on a table so that all the values and suits are visible. The cards are spread along a line and not along a circle so cards in position 1 and 52 are not next to each other. (a) (1 point) What is the probability of a macrostate of the deck where exactly one pair of cards of the same value and same color are located next to each other somewhere in the deck? (b) (1 points) What is the entropy of the microstate in (a)? (c) (1 points) What is the probability of a macrostate of the deck where at least one pair of cards of the same value and same color are located next to each other somewhere in the deck? (d) (1 points) What is the entropy of the microstate in (c)? (e) (1 points) What is the probability of a macrostate of the deck where exactly one pair of cards of the same value (any color) are located next to each other somewhere in the deck? (f) (1 points) What is the entropy of the microstate in (e)?