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You are randomly dealt 5 cards from a standard deck of 52 playing cards. What is the probability that you have at least 4 cards of the same suit?

My solution:

4 [ P(4 of the same suit) ] - because there are 4 different ways to get 4 of the same suit, Clubs, Hearts, Spades and Diamonds.

P(4 of the same suit) =
(13 C 4 * 39 C 1)/
(52 C 5)

13 Choose 4 because you have 13 different cards in one suit, and you must choose 4 of those, then for the remaining 39 cards you must choose 1.

4 [ P(4 of the same suit) ] = .0429

Does this seem like I answered the question properly?

  • Math -

    you forgot the case where all 5 are of the same suit
    "at least 4 of the same suit" means it could be 4 of the same suit or it could be 5 of the same suit.

    which would be 4(13C5)/52C5

    add that on to your answer

  • Math -

    That seems to make sense to me. Thank you Reiny

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