9/1/2021

See Collector.pdf on our Google Drive folder for copies of discussion from last class.

See Prisoner.pdf on our Google Drive folder for my solution to the prisoner's dilema from last class.

Chapter 1 Combinatorial Analysis (Counting) Section 1.1. Equally Likely Outcomes

• Multiplication Principle
  • Application 1 - Rolling Dice
  • Application 2 - Tossing a Coin k times
• Permutations
• Combinations
  • Example 1 - In how many ways can I arrange 8 students into 8 chairs?
  • Example 2 - In how many ways can I put 8 students into 3 chairs?
  • Example 3 - Suppose there are 4 women and 4 men and I am interested in filling the three chairs in the following way: Woman-Man-Woman. In how many ways can I do this?
  • Example 4 - How many permutations exist for the letters in the word statistics?
  • Example 5 - Consider a bowl which contains 6 ping pong balls numbered 1, 2, 3, 4, 5, and 6. If we sample 3 balls without replacement,
    • how many sequences of outcomes are possible?
    • What is the probability that the first ball is a 2?
    • What is the probability that the first ball is i (for i=1, 2, ..., 6)?
    • What is the probability that the second ball is i (for i = 1, 2, ..., 6)?
  • Example 6 - A personnel officer has available 8 candidates, five men and three women, to fill 4 positions. If every combination of candidates is equally likely to be chosen, what is the probability that no women will be hired?
  • Example 7 - How many committees are possible from a group of five individuals when the size of the committee is unspecified

Please complete your reading of Chapter 1 for Friday. Our first Problem Session will be on Friday