Question

7. There are 52 playing cards; let S be the set of all of them. A "deck" is a particular order (or permutation) of the 52 cards. Mathematically, a deck can be represented by (ci,, 2) where ci,c2,., cs2 are all the elements of S. The interpretation is that ci is the first card in the deck, c2 is the second card, and so on. Let 2 be the set of all possible decks. a) Is Ω a subset of S52? Is S52 a subset of Ω? b) A deck of cards is distributed to four players (Adam, Bob, Chris and David), each receiving 13. The set of all cards that a player receives is called his hand. Let A be the set of possible hands of Adam. Is A a subset of Ω? Is A a subset of S52? Is A a subset of S13? c) Here is how the cards are distributed. Players take cards in the cycle Adam-Bob-Chris-David-Adam- Each player takes one card when it is his turn. (For example, Adam takes the first card, Bob takes the second, Chris takes the third, David takes the fourth, and then Adam takes the fifth.) Givena deck (c1, C2, ,C52), what is Adam's hand? d) What is the subset of 2 corresponding to the event that Adam has A (Ace of diamond)? e) What is the subset of S2 corresponding to the event that Adam has both A and K?

Answer 1

Griven no.of cands.52 st cand in the deck is C g nd cand in the deck is C and So o)n a) CES CIfC ,52 S2. 52 Given the deck (ace s, Adam's s the d) The Subsel Ehat conespondstothe event that Adam has ace diamord is this fonn3

2 K1 I e) The suhset af J2 thak Adan has both A and k 4k-Hi 4Kt