Counting Principles NMH Upward Bound Summer Academy Statistics
Counting Principles NMH Upward Bound Summer Academy Statistics H. Reardon
Fundamental Counting Principle Ø For a sequence of two events in which the first event can occur m ways and the second event can occur n ways, the events together can occur a total of m • n ways. ØThe fundamental counting principle extends to situations involving more than two events. ØWhen you have the same event x happening y times (such as an alarm system code or a padlock), do xy for a shortcut to the total number of ways.
Example Ø You finished college and are looking to buy your first car. There are two styles: sedan or SUV; five colors: black, red, green, blue, or yellow; and three models: standard, sports, and luxury. How many possible combinations are there? Ø 2 styles • 5 cars • 3 models = 30 total car choices
Factorial Rule Ø A collection of n different items can be arranged in order n! different ways. ØExample: You have 6 textbooks on a bookshelf. How many different can you arrange these 6 textbooks? Ø 6! = 6 · 5 · 4 · 3 · 2 · 1 = 720 different ways
Permutations •
Example •
Combinations •
Example •
License Plates Ø In California, drivers of normal cars who do not elect to have a custom license plate (which is expensive) will have a license plate assigned to them. The plate consists of 7 places: one digit 0 -9, followed by three letters A-Z, followed by three digits 0 -9. How many possible license plates are there? ØHow many ways can you arrange three letters in the middle? ØThis only applies to passenger cars. Flatbed trucks have a different system. Motorcycles another. Commercial vans yet another. Why do you think there are so many possible permutations?
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