Consider a standard deck of 52 playing cards. There are 13 cards of each suit (clubs , diamonds , spades , hearts ). Now, suppose a microstate is a specific ordering of the cards. There are thus 52! possible microstates . Calculate the multiplicities of the following macro-states (going from easier to harder):

a) The top card of the deck is the queen of hearts (Q)

(b) The first two cards are clubs ().

(c) The first 26 cards are all red, the last 26 are all black.

(d) The cards alternate in color (starting from either red or black)

(e) The first 5 cards contain a royal flush of any suit. A royal flush is the 5 most valuable cards of a single suit (e.g. 10, J, Q, K, and A). The 5 cards can be in any order! In all cases, you should use the factorial (!) and/or "n choose k