Consider a standard deck of 52 cards. Suppose we draw 5 cards at random. How man
ID: 3201435 • Letter: C
Question
Consider a standard deck of 52 cards. Suppose we draw 5 cards at random. How many possible outcomes (microstates) are there? (Assume that you keep track of the order in which you draw the cards, so 9H followed by 4C is not the same as 4C followed by 9H.) Now consider the set of macrostates defined by just considering the final 5-card hands, ignoring the order in which you drew the cards. How many of these macrostates are there? What is the distribution of their multiplicities? Now consider a new macrostate: flush (all 5 cards of the same suit). What is its multiplicity? Look up the probability of drawing a 5-card flush and check that your answer is correct.Explanation / Answer
a.) Possible outcomes = 52*51*50*49*48 = 311,875,200
52 => you can draw first card in 52 ways
51 => you can draw second card in 51 ways
50 => you can draw third card in 50 ways
49 => you can draw fourth card in 49 ways
48 => you can draw fifth card in 48 ways
b) One card can appear on five places but we want to have it at only 1 place because order does not matter only final 5 cards matter.
Possible outcomes = 52*51*50*49*48 / (5*2) = 31,187,520
Multilicity = 10
c) Possible outcomes = 4*13*12*11*10*9 = 617,760
P = (1/4)*(13/52)*(12/51)*(11/50)*(10/49)*(9/48) = 0.000124