Sample Exercise

1. In how many ways can we select three officers out of 9 men and 7 women,
   such that both sexes are represented?
2. A club consists of 8 men ane 5 women. In how many ways can we select
   a president and a secretary?
3. A club consists of 10 men ane 7 women. We want to select a president,
   a secretary, and a treasurer. What is the probablilty that all these three
   officers have no woman.
4. Five manufacturers produce a certain electronic device, whose quality varies from
   manufacturer to manufacturer. If you were to select three manufacturers at random,
   what is the chance that the selection would contain exactly two of the best three?
5. Four microprocessors are randomly selected from a lot of 10 microprocessors
   among which 3 are defective. Find the probability of obtaining no defective
   microprocessors.

Rules

1. If order is important, use permutation, else use combination.
2. AND - apply multiplication rule.
3. OR - apply addition rule but do not duplicate it.
4. Permutation fomula:

   Pnr = n! / (n-r)!

5. Combination formula:

   Cnr = n! / (r!*(n-r)!)

6. Probability = number of elements in Event / number of elements in Sample spaces,
   where Event is the set of what you are insterested,
   Sample Space is the set of all possible outcomes.