Problems involving both permutations and combinations

Problems involving both permutations and combinations

Lessons

  • 1.
    From a standard deck of 52 cards, how many 5-card poker hands can be formed in each case:
    a)
    straight flush - 5 cards in sequence, all of the same suit, e.g. 6, 7, 8, 9, 10?

    b)
    four of a kind?

    c)
    full house - 3 of a kind and a pair, e.g. 5, 5, 5, 8, 8?

    d)
    flush - all 5 cards are of the same suit?

    e)
    straight - 5 cards in sequence, but not all of the same suit, e.g. 2, 3, 4, 5, 6?

    f)
    three of a kind?

    g)
    two pairs?

    h)
    one pair?

    i)
    high card?

    j)
    show that the sum of all 9 categories of 5-card hands (from straight flush to high card) equals the number of all 5-card hands.