1. What is the probability of getting at least 1 diamond in a 5-card hand dealt from a standard 52-card deck?
2. In a family with 3 children, excluding multiple births, what is the probability of having 2 boys and 1 girl, in any order? Assume that a boy is as likely as a girl at each birth.
3. A country park system rates its 20 golf courses in increasing order of difficulty as bronze, silver, or gold. There are only two gold courses, and twice as many bronze as silver.
a. If a golfer decides to play a round at a silver or gold course, how many selections are possible?
b. If a golfer decides to play one round per week for 3 weeks, first on a bronze course, then silver, then gold, how many combined selections are possible?
4. In the next 2 questions, would you consider the selection to be a permutation, a combination, or neither? Explain your reasoning:
a. The new university president named 3 new officers: a vice-president of finance, a vice-president of academic affairs, and a vice-president of student affairs.
b. A student did some holiday shopping by buying 4 books: 1 for his father, 1 for his mother, 1 for his young sister, and 1 for his older brother.
This provides several examples of solving probability problems and working with counting techniques.