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.
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Solution contains calculations of probabilities.
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