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9.5 Problems

1. The marketing department has asked how many product permutations are possible for a new product. The product will hold three colored balls. In total there are 6 ball colors available. If balls must be used in all spots, and ball colors can be used more than once how many permutations are possible? (ans. 216)

2. A worker is packing small cereal boxes into a larger box. If the worker is picking from a set of 10 different cereal boxes, but can only place 8 in the larger box, how many combinations are possible? (ans. 45)

3. An assembly operation places two parts a board. There is a 3% chance that part A is bad, and a 2% chance that part B is bad. What is the chance the board contains a bad part? (ans. 4.94%)

4. How many ways could 5 operators be assigned to 5 workstations? (ans. 120)

5. How many ways could 8 operators be assigned to 5 workstations? (ans. 6720)

6. There are nine product, each a different color. They are to be put into 3 boxes each holding 3 products. a) How many unique package arrangements are possible? b) How many different combinations of packaged products are possible if the position does not matter? (ans. a) 362,880 b) 1680)

7. An electronics company will assemble circuit boards with interchangeable components. There are 3 places to mount the components and there are 5 types of components. Each component type may only be used once. How many different outcomes are possible? (ans. 60)

8. A toy is being manufactured to have prizes in 2 of 5 slots. How many prize layouts are possible? (ans. 10)

9. Calculate the following values.

10. There are 8 machines (A to H) waiting to be shipped. 3 of these will be tested.

a) How many combinations are possible?

b) How many of those combinations contain machine C?

c) How many combinations contain A or H, but not both?

d) If 2 trucks are loaded with 4 machines, how many distributions are possible?

e) Resolve part d) if machine A and B are in the same truck.

(ans. a) 56, b) 21, c) 30, d) 70, e) 15)

11. A carton contains 12 parts, 4 are red and 8 are green.

a) Find the probability that the first part removed is green.

b) If 3 parts are removed what is the probability that all are red?

c) Repeat b) for all green.

d) Repeat b) for one red and 2 green.

(ans. a) 2/3, b) 1/55, c) 14/55, d) 28/165)

12. Write routines to implement basic functions.