Probability involving permutations and combinations

Lessons

• Introduction
  Two cards are picked without replacement from a standard deck of 52 cards.
  Determine the probability that both cards are queens using:
  
  a)

  the multiplication rule
  
  
  b)

  combinatorics
  
  

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• 1.
  Three prizes are awarded in a raffle to a class of 25 students. Each student holds one ticket.
  
  a)

  If the raffle has three identical prizes, what is the probability that Amy, Ben, and Calvin are the 3 prize winners?
  
  
  b)

  What is the probability that Amy, Ben, and Calvin win first prize of $100, second prize of $20, and third prize of $5, respectively?
  
  

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• 2.
  A class has 6 girls and 4 boys. A committee of 3 is to be randomly selected. What is the probability of each event?
  
  a)

  All 3 people selected are girls.
  
  
  b)

  Only 1 person selected is a girl.
  
  
  c)

  At least 2 people selected are boys.
  
  

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