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March 25, 2017

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Five cards are drawn at random without replacement from and ordinary deck of 52. What is the probability all 5 cards are from the same suit?

  • Statistics - ,

    1 of the 4 suits ---> C(4,1) = 4
    5 from one of those suits = C(13,5) ---> 1287
    5 from the whole deck ---> C(52,5) = 2598960

    so prob = 4(1287)/2598960
    = 33/16660 = .00198

  • Statistics - ,

    I'm confused as to how you're getting these numbers... Could you possible break it down a little farther please? I don't understand how you get from C(52,5)=2598960...Thank you so much for helping!

  • Statistics - ,

    Have you learned the difference between permutations and combinations?
    in combinations the order does not matter.
    (if I hold 5 cards in my hand, the order in which they were dealt to me does not matter)

    C(13,5) means ..
    how many groups of 5 can I form from 13
    It is short form for 13!/(5!8!)
    = 13x12x11x10x...x2x1/(8x7x6x..x2x1)(5x4x3x2x1))
    = 13x12x11x10x9/(5x4x3x2x1) = 154440/120 = 1287

    On your calculator there is a button labeled
    nCr

    so enter
    13
    2nd F
    nCr
    5
    =

    You should get 1287

  • Statistics - ,

    253/9996

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