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# Probability and counting rules

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1. In a board of directors composed of 8 people, how many ways can 1 chief executive officer, 1 director, and 1 treasure be selected. Answer the question, and show your method.

2. The general manager of a fast food restaurant chanin must select 6 resturants from 11 for a promotional program. How many different possible ways can this selection be done. Answer the question, and show your method.

3. How many ways can a jury of 6 women and 6 men be selected from 10 men and 12 women in a golf club. Answer the question, and show your method.

4. An advertising manager decides to have an ad campaign in which 8 special calculators will be hidden at various locations in a shopping mall. If he has 17 locations from which to pick, how many different possible combinations can he choose. Answer the question, and show your method.

5. A parent teacher committee consisting of 4 people is to be formed from 20 parents and 5 teachers. Find the probability that the committee will consist of these people (assume that the selection will be random). Show your method and answer for each part.

(a) all teachers

(b) 2 teachers and 2 parents

(c) all parents

(d) 1 teacher and 3 parents

6. A package contains 12 resistors, 3 of which are defective. If 4 are selected, find the probability of getting. Show your method and answer for each part.

(a) no defective resistors

(b) 1 defective resistor

(c) 3 defective resistors

7. An insurance sales representative selects three policies to review. The group of policies she can select from contains 8 life policies, 5 automobile policies, and 2 homeowner's policies. Find the probability of selecting. Show your method and answer for each part.

(a) all life policies

(b) both homeowners policies

(c) all automobile policies

(d) 1 of each policy

(e) 2 life policies and 1 automobile policy

8. Find the probability of randomly selecting 2 mathematics books and 3 physics books from a box containing 4 mathematics books and 8 physics books. Show your method and your answer.