3 c62 8 22 page 20115 we must classify the possible

This preview shows page 4 - 7 out of 14 pages.

3! + C(6,2) 8! 2!2! ). page 201,15. We must classify the possible types of five letter “words”. type I. Four letters of one kind and another different letter. type II. Three letters of one kind and two of another. type III. Three letters of one kind and two other letters each of a different kind. type IV. Two letters of one kind, two letters of another kind and one other letter. type V. Two letters of one kind, and three different letters. Mississippi has one M, four I’s , four S’s and two P’s.
Image of page 4

Subscribe to view the full document.

5 For type I, there are C(2,1) x C(3,1) x 5 4 ! ! such “words”. For type II, there are C(2,1) x C(2,1) x 5 3 2 ! ! ! such “words”. For type III, there are C(2,1) x C(3,2) x 5 3 ! ! such “words”. For type IV, there are C(3,2) x C(2,1) x 5 2 2 ! ! ! such “words”. For type V, there are C(3,1) x 5 2 ! ! such “words”. Using the “or” principle, our answer will be the sum of all these cases. 8. page 189, 12 A standard 52 card deck has 13 types of cards, each type comes in four suits. a. The number of five-card poker hands with four aces, is C(4,4) x C(48,1). C(4,4) counts the number of ways to select four aces out of the four aces available. After the four aces are selected there are C(48,1) ways to select a non-ace. b. The number of five-card poker hands with four of a kind is C(13,1)xC(4,4)xC(48,1). From thirteen types of cards, pick one of them, i.e. C(13,1) ways, next pick four of the four cards of available of that type, i.e. C(4,4) ways, and with the forty-eight cards left pick one them, i.e. C(48,1) ways. c. The number of five-card poker hands with exactly two different pairs is C(13,2) x C(4,2) x C(4,2) x C(44,1). From thirteen types of cards, pick two of them, i.e. C(13,2) ways, next pick two of the four cards available of the first type, do the same with the second type, i.e. C(4,2) x C(4,2) ways to do both, and with the forty-four cards remaining select one more ,i.e. C(44,1) ways.
Image of page 5
6 d. The number of five-card poker hands that are a full house is C(13,1)xC(4,3)xC(12,1)xC(4,2). From thirteen types of cards, pick one of them which will form the three of a kind, i.e. C(13,1) ways, next select three cards from the four available of this type. There are now twelve types of cards left, pick one of them to form the two of a kind, i.e. C(12,1) ways, next select two of the four cards available of this type. e. There are nine possible ways to get consecutive values. They are 2 3 4 5 6, 3 4 5 6 7, 4 5 6 7 8, 5 6 7 8 9, 6 7 8 9 10, 7 8 9 10 J, 8 9 10 J Q, 9 10 J Q K, 10 J Q K A. Each sequence can be obtained in C(4,1)xC(4,1)xC(4,1)xC(4,1)xC(4,1) ways, because each card comes in four suits. Using the “or” principle, we sum all of these up, and get 9 x 4 5 as our answer. Note that this answer includes straight flushes. f. The number of five-card poker hands that have no pairs, is C(13,5)xC(4,1)xC(4,1)xC(4,1)xC(4,1)xC(4,1) ways. From the thirteen types of cards available, choose five of them, i.e. C(13,5) ways. From each of the types you selected, choose one card from each.
Image of page 6

Subscribe to view the full document.

Image of page 7
You've reached the end of this preview.
  • Fall '06
  • miller
  • Numerical digit, ways

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern