Answer
In order of increasing probability, the macrostates are b, a, c, d.
Work Step by Step
We draw five cards from the deck. The problem asks for the number of microstates corresponding to each of the four macrostates.
a. There are only four microstates corresponding to this macrostate: 4 aces plus the king of hearts, 4 aces plus the king of diamonds, 4 aces plus the king of spades, and 4 aces plus the king of clubs.
b. There is only one microstate corresponding to this macrostate: the exact 4 cards specified.
c. There are 144 microstates corresponding to this macrostate.There are 6 ways to pick a pair of jacks (club+diamond, heart+diamond , spade+club, spade+heart, spade+diamond, club+heart), and six ways to pick a pair of queens. Also, there are four possible aces. In summary, the number of microstates is (6)(6)(4) =144.
d. There are many microstates. There are 52 possibilities for the first card, then 48 possibilities for the second card so that it doesn’t equal the first card, 44 for the third, 40 possibilities for the fourth, and 36 for the fifth. In summary, the number of microstates is (52)(48)(44)(40)(36) =158,146,560.
In order of increasing probability, the macrostates are b, a, c, d.
