9/5/2012

See Collector.pdf for copies of discussion 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

Our first Problem Session will be on Friday