A rapidly growing city is dedicated to neighborhood integrity. However, increasing traffic and speed on a through street are of concern to residents. The city manager has proposed five independent traffic-calming options:

1. Stop sign at corner A
2. Stop sign at corner B
3. Low-profile speed bump at point C
4. Low-profile speed bump at point D
5. Speed dip at point E
There cannot be any of the following combinations in the final projects:
—No combination of dip and one or two bumps
—Not two bumps
—Not two stop signs
(a) If there were no restrictions on how the op­tions can be combined, calculate how many alternatives there are to evaluate.
(b) Using the restrictions, identify the number of and list of acceptable alternatives.


(a) Total possible = 2? = 32

(b) Because of restrictions to combinations of 3, 4, or 5, only 12 remain acceptable:
DN, 1, 2, 3, 4, 5, 1&3, 1&4, 1&5, 2&3, 2&4, and 2&5.

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