This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 1 Homework 4 (11.5 points) due Feb. 10 (1 pt.) 3.34ab A club has 14 members. a) How many ways can a governing committee of size 3 be chosen? This is without replacement because once a person is on the committee; he cant be on it again. This is unordered because there are no individual titles to the members on the committee. N(E) = 14 3 = 14! 14 3 !3! = 14! 11!3! = 14 13 12 3! = 364 b) How many ways can a president, vice president, and treasurer be chosen? This is without replacement for the same reason. This is ordered because the president, vice president and treasurer are distinct positions. N(E) = (14) 3 = 14! 14 3 ! = 14! 11! = 14 13 12 = 2184 = 14 3 3! = 14! 14 3 !3! 3! (2.5 pts.) 3.36 (abdef only) (I will post the answers to all of the parts for your personal information :) (p.107) In fivecard draw, the order of the cards is not important. In addition, aces can either be high or low, that is the order is: ace, 2, 3, , jack, queen, king, ace. Determine the number of possible hands of the specified type. a) straight flush: five cards of the same suit in sequence N(E) = (the number of ways that 1 suit can be chosen) times (the number of possible ending or starting cards of the straight). We have 14 numbers in a suit because Ace can be either high or low. = 4 1 14 5 + 1 = 4 10 = 40 b) Four of a kind: {w, w, w, w, x}, where w and x are distinct denominations. N(E) = (the number of ways that 1 number can be chosen from the numbers) times (the number of ways that 4 cards can be chosen from 4 cards) times (the number of ways that 1 card can be chosen from the rest of the deck) = 13 1 4 4 52 4 1 = 13 1 48 = 624 d) flush: five cards of the same suit, not all in sequence N(E) = (the number of ways that 5 cards can be chosen from the suit) times (the way that 1 suit can be chosen from all of the suits)  (the number of straight flushes (part a)) = 13 5 4 1 40 = 13! 13 5 ! 5! 4 40 = 13! 8! 5! 4 40 = 5148 40 = 5108 2 e) straight: five cards in sequence, not all of the same suit N(E) = (the number of possible ending cards of a straight see part a) times (the number of ways that 1 number can be chosen from 4 numbers repeated 5 times)  (the number of straight flushes (part a)) = 10 4 1 4 1 4 1 4 1 4 1 40 = 10 4 5 40 = 10,240 40 = 10,200 f) three of a kind: {w, w, w, x, y}, where w, x and y are distinct denominations N(E) = (the number of ways that 1 number can be chosen from all of the numbers) times (the number of ways that 3 cards can be chosen from 4 cards) times (the number of ways that 2 cards can be chosen from the nonw numbers in the deck  unordered) times (the number of ways that 1 number can be chosen from 4 suits repeated twice)....
View Full
Document
 Spring '08
 Staff

Click to edit the document details