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.
  
  

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