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 * Aim:** How do we solve problems using permutations?

At the end of the lesson, you will be able to...
 * 1) define permutation, factorial (!), nPn = n!, and nPr
 * 2) apply factorials to compute the number of arrangements of n different objects taken n at a time
 * 3) compute the number of permutations of n things taken n at a time
 * 4) employ the notation nPr in solving problems involving n things taken r at a time
 * 5) compute the number of permutations involving n things taken r at a time
 * 6) discover a formula for the number of permutations of n objects taken r at a time
 * 7) apply the counting principle along with permutations to count the elements in a sample space
 * 8) use the calculator to compute permutations and factorials
 * 9) use permutations with and without the counting principle to determine the probability of an event

Here are some questions you can canswer as you follow along with the video. Copy them into your notebook first before you begin.
 * 1) What symbol is used for factorial?
 * 2) What is a permutation?
 * 3) When should we use permutations?
 * 4) How can we use our graphing calculators to find a value of a factorial?
 * 5) How can we use out graphing caluclators to find a value of a permutation?
 * 6) P(n,r) is on way to write a permutation. What is another way to write a permutation?
 * 7) How does permutation with repetition differ from permutation without repetition?


 * Video**

media type="youtube" key="JyRKTesp6fQ" width="425" height="350"

1. In how many ways can the letters of the word PENCIL be arranged? (Ans: 6P6 or 6! = 720) 2. In how many different ways can the letters of the word PENCIL be arranged if the first letter is a constant? (Ans: 4 X 5P5 = 480) 3. Helene is lining up beads to plan a necklace. She has a total of 36 beads and 32 of the are identical. How many different arrangements of the 36 beads can she make? (36!/32! = 1413720) 4. A music teacher is arranging a recital for her students. There are 7 students, each with her own instrument: 3 play the piano, 2 play the violin, 1 plays the flute, and 1 plays the cello. In how many ways can the order of the instruments be arranged? (Ans: 7!/(3! x 2!) = 420)
 * Classwork:** Answer each question.


 * Homework:** No homework with this lesson. It will be part of the next lesson.


 * Journal entry:** Explain the meaning of permutation. Make up a problem in which the permutation formula would be used to solve it.