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How many ways can you draw 3 queens and 2 kings from a deck of 52 cards?

  1. Mar 14, 2009 #1
    How many ways can you draw 3 queens and 2 kings from a deck of 52 cards?
     
  2. jcsd
  3. Mar 14, 2009 #2

    arildno

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    You are to pick out 5 cards out of 8 possible ones; three queens out of the four possibles, and two kings out of the 4 possibles.

    Start with:

    Out of 4 kings, how many 2-king combinations exist?
     
  4. Mar 14, 2009 #3
    2, i guess?
     
  5. Mar 14, 2009 #4

    arildno

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    Do not guess, think.
     
  6. Mar 14, 2009 #5
    ok 2 ... coz there are 4 kings in a deck of 52 cards....
     
  7. Mar 14, 2009 #6

    arildno

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    No.

    Try to think again. LOGICALLY. It isn't too hard.

    First sub-question: How many 2-sets of kings exist if the king of spades is to be included?

    Second sub-question: How many 2-sets of kings exist if the king of spades is NOT included?
     
  8. Mar 14, 2009 #7

    tiny-tim

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    since there's only 4 of them …

    call them A B C and D, and write out all the possible pairs :wink:
     
  9. Mar 14, 2009 #8
    2 if the king of spades is included and 1 if it is not.
     
  10. Mar 14, 2009 #9

    arildno

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    This won't work, diceyfume.

    You are obviously refusing to utilize your intellect, and are only interested in being spoonfed "answers".

    I strongly advise you to quit maths, because your attitude makes you incompetent in it.
     
  11. Mar 14, 2009 #10
    6 , ab, bc, cd, ad, ac, bd
     
  12. Mar 14, 2009 #11

    arildno

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    Correct. Why didn't you start doing that on your own?

    Now, how many sets of three queens can you form out of 4?
     
  13. Mar 14, 2009 #12
    i guess its 6... i posted it... thanks, i'll just try next sem..
     
  14. Mar 14, 2009 #13
    6 possibles for king right? and for queen how many?
     
  15. Mar 14, 2009 #14

    tiny-tim

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    d'oh! :rolleyes:

    call them A B C and D, and list the ways!​
     
  16. Mar 14, 2009 #15
    for the queen, abc,bcd, cda? am i corrct?
     
  17. Mar 14, 2009 #16

    tiny-tim

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    Nooo :rolleyes:
     
  18. Mar 14, 2009 #17
    abc,bcd, cda, abd.... it's 4?
     
  19. Mar 14, 2009 #18

    arildno

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    Right!

    So, you have 6 2-sets of kings, and 4 3-sets of queens.

    So, how many different combinations consisting of one king-set and one queen set can you then make?
     
  20. Mar 14, 2009 #19
    abc. abd, cda, bcd, it's 4?
     
  21. Mar 14, 2009 #20

    tiny-tim

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    Yes, it's 4 …

    but you can't list them like that in an exam :wink:, so what formula would you show the examiner (and what formula for the 6 ways of the kings)?
     
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