Finite Math

posted by .

A "hand" consists of a set of 5 cards selected from an ordinary deck of 52 cards:

(1) How many different hands contain exactly 4 diamonds? = 27885

(2) How many different hands contain exactly 4 cards of the same suit (any of the four suits)?

(3) How many different hands contain cards of exactly one suit?

Can someone help me figure out the last two questions?

  • Finite Math -

    so you want 4 out of the 13 diamonds ---> C(13,4)
    then one more card from the 39 non-diamonds --> C(39,1)
    so 715x39 = 27885

    2. wouldn't the answer to 1. which was for diamonds be the same for the clubs, the same for the hearts, and the same for the spades ???
    so 4x27885

    3. I assume the suit would be specified.
    If not, then for each specific suit is would be C(13,5) = 1287 , that is, all 5 cards come from the same 13 cards.

  • Finite Math -

    Thanks Reiny!!!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math - combinations

    Each hand in the game of bridge has 13 cards dealt from a regular deck of 52 cards. a) How many different bridge hands are possible?
  2. probability

    of the 2598960 different 5 card hands possible from a deck of 52 playing cards, how many would contain all 4 tens?
  3. math

    In a card game using a normal deck of playing cards containing 52 cards, 13 cards are dealt to a player. a) how many different combinations of cards are possible in that players hands?
  4. Algebra

    How many hands of 5 cards can be made from a standard deck of cards such that each hand contains exactly 1 red card and 4 black cards?
  5. Algebra

    Hi, can I have some help with my permutation/combination homework?
  6. Maths

    A standard pack of 52 cards consists of 4 suits, hearts, diamonds, clubs and spades. Each suit has 13 cards, from Ace to King. We deal randomly 5 cards from the deck of 52. 2 deals differing only by the order are considered the same. …
  7. Statistics

    A standard pack of 52 cards consists of 4 suits, hearts, diamonds, clubs and spades. Each suit has 13 cards, from Ace to King. We deal randomly 5 cards from the deck of 52. 2 deals differing only by the order are considered the same. …
  8. Statistics

    Select three different five card combinations or five-card hands from your favorite card game that utilizes a standard 52-card deck containing four suits (clubs, hearts, diamonds, and spades), with each suit containing 13 cards with …
  9. statistics

    Select three different five card combinations or five-card hands from your favorite card game that utilizes a standard 52-card deck containing four suits (clubs, hearts, diamonds, and spades), with each suit containing 13 cards with …
  10. Statistics

    Can someone please explain this to be, so that I can understand this problem?

More Similar Questions