Eight players play a card game with a 52 card deck The deck

Eight players play a card game with a 52 card deck. The deck is shuffled and each player is dealt four cards.

a.) What is the probability that player A gets all four kings?

b.) What is the probability that some player gets all four kings?

c.) What is the probability that player A gets four cards of a kind? (That is, four aces, four kings, four queens, ... four aces.)

d.) What is the probability that some player gets four cards of a kind? Why is it a lot harder to go from answer c. to answer d. than it was to go from answer a. to answer b.?

Solution

a. Player A can get 4 cards in 52C4 ways.

Player A can get 4 kings in 1 way, i.e probability of getting four king is 1/52C13

B. Probability that some player gets 4 king is,

P(player gets 4 kings) + P(player B gets 4 KINGS) + P(player C gets 4 kings)+p(player D gets 4 kings)=4/52c13