Congratulations! You have won a free trip to Europe. On your trip you have the opportunity to visit 6 different cities. You are responsible for planning your European vacation. How many different ways can you schedule your trip? The answer may surprise you!
This is an example of a permutation.
How many ways can you visit the European cities? There are 6 choices for the first stop. Once you have visited this city, you cannot return so there are 5 choices for the second stop, and so on.
There are 720 different ways to plan your European vacation!
Solution: This equation asks, “How many ways can 6 objects be chosen 3 at a time?”
There are 6 ways to choose the first object, 5 ways to choose the second object, and 4 ways to choose the third object.
There are 120 different ways 6 objects can be chosen 3 at a time.
Permutations and Graphing Calculators
Most graphing calculators have the ability to calculate a permutation.
Permutations and Probability
The letters of the word HOSPITAL are arranged at random. How many different arrangements can be made? What is the probability that the last letter is a vowel?
There are eight ways to choose the first letter, seven ways to choose the second, and so on. The total number of arrangements is 8!= 40,320.
There are three vowels in HOSPITAL; therefore, there are three possibilities for the last letter. Once this letter is chosen, there are seven choices for the first letter, six for the second, and so on.
Probability, as you learned in a previous chapter, has the formula:
There are 15,120 ways to get a vowel as the last letter; there are 40,320 total combinations.
Multimedia Link: For more help with permutations, visit the http://regentsprep.org/REgents/math/ALGEBRA/APR2/LpermProb.htm - Algebra Lesson Page by Regents Prep.
- Define permutation.
In 2 – 19, evaluate each permutation.
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