Data 605 Week 7 Discussion

40. A bridge deck has 52 cards with 13 cards in each of four suits: spades, hearts, diamonds, and clubs. A hand of 13 cards is dealt from a shuffled deck. Find the probability that the hand has

1. a distribution of suits 4, 4, 3, 2 (for example, four spades, four hearts, three diamonds, two clubs).

sp <- factorial(13)/(factorial(9)*factorial(4))
ht <- factorial(13)/(factorial(9)*factorial(4))
di <- factorial(13)/(factorial(10)*factorial(3))
cl <- factorial(13)/(factorial(11)*factorial(2))
all<- factorial(52)/(factorial(39)*factorial(13))

p <- round((sp*ht*di*cl/all),4)

The probability is of being dealt 4 spades, 4 hearts , 3 diamonds and 1 club is 1.8%

2. a distribution of suits 5, 3, 3, 2.

sp <- factorial(13)/(factorial(8)*factorial(5))
ht <- factorial(13)/(factorial(10)*factorial(3))
di <- factorial(13)/(factorial(10)*factorial(3))
cl <- factorial(13)/(factorial(11)*factorial(2))
all<- factorial(52)/(factorial(39)*factorial(13))

p <- round((sp*ht*di*cl/all),4)

The probability is of being dealt 5 spades, 3 hearts , 3 diamonds and 1 club is 1.29%