Combinations

Lessons

• 1.
  Compare the difference between the following 2 scenarios:
  a)

  How many ways can a president, a vice president, and a treasurer be selected from a class of 20 students?
  
  
  b)

  How many different committees of 3 people can be selected from a class of 20 students?
  
  

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• 2.
  A standard deck of 52 cards consists of:
  • 4 suits: diamonds, hearts, spades, and clubs
  • each suit has 13 cards
  • red cards: diamonds and hearts
  • black cards: spades and clubs
  • face cards: Jacks, Queens, and Kings
  How many different 5-card hands can be formed containing:
  a)

  any 5 cards (no restrictions)?
  
  
  b)

  all black cards?
  
  
  c)

  1 black card and 4 red cards?
  
  
  d)

  all face cards?
  
  
  e)

  3 Jacks and 2 Kings?
  
  
  f)

  3 Jacks?
  
  

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• 3.
  Problems with "at least", "at most"
  From a standard deck of 52 cards, how many different 5-card hands can be formed containing:
  a)

  exactly 2 Diamonds?
  
  
  b)

  at least 2 Diamonds?
  
  
  c)

  at most 2 Diamonds?
  
  

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• 4.
  There are 20 members in a student council, 7 boys and 13 girls. How many ways can a committee of 5 people be selected if there must be:
  a)

  at least 3 boys?
  
  
  b)

  at most 1 girl?
  
  
  c)

  at least 1 girl?
  
  
  d)

  at least 2 boys and 2 girls?
  
  

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• 5.
  Five points are marked on a circle. By connecting the points on the circle,
  a)

  How many triangles can be formed?
  
  
  b)

  How many line segments can be formed
  
  
  c)

  Form a pentagon inside the circle by connecting the 5 points. How many diagonals does the pentagon have?
  
  

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