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# 10.1 n!

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### 10.1 n!

1. 1. Opener: Agenda (Algebra 2) •Opener (5 mins)The digits 1, 2, 3, 4, 5, 6 and 7 are used to generate a •LE 10.1Four-digit customer code. How many different •Assignment #2codes are possible if the first two digits must beeven numbers and the last two digits must be oddnumbers and repetition is allowed? Materials Needed •activotes Reminders •Ch.10 Test scheduled for Mar 30A+M=P:
2. 2. LE 10.1 Introduction of Permutation WofD:n factorial,LO: What is a permutation? permutation An arrangement of n distinct objects in a specific order is called a permutation. The number of ways to arrange: •n objects using ALL n objects without repetitions is n! •n objects using ALL n objects with repetitions is n! s!⋅s! s! NOTE: This is also referred to as By definition: distinguishable permutation 0! = 1 (with reps)
3. 3. A) 720 C) 14 A) 6 C) 132B) 10,080 D) 1,200 B) 2 D) 240
4. 4. Model Skill “I DO” Scaffold Skill “WE DO”Example: ExampleHow many ways can I arrange 5 students In how many different ways can 4 teams finish a competition (assuming there arein line? no ties)?Solution: SolutionMethod 1: FCP ___ x ___ x ___ x ___ x ___ S1 S2 S3 S4 S5Method 2: Permutation
5. 5. Guided Practice “YOU DO”ExampleYou need to arrange seven of your favorite books along a small shelf. How manydifferent ways can you arrange the books, assuming that the order of the booksmakes a difference to you?A) 5040 B) 7 C) 823,543 D) 840
6. 6. Model Skill “I DO” Scaffold Skill “WE DO”Example: ExampleHow many different ways can the letters How many different ways can the lettersin MATH be arranged? in MISSISSIPPI be arranged?Solution: Solution
7. 7. Guided Practice “YOU DO”ExampleHow many 3 digit numbers can be formed using only odd digits from 1 through 9,with repetition allowed?A) 15 B) 7 C) 27 D) 125
8. 8. Guided Practice “YOU DO”ExampleYou have 4 flower pots on a window seal, how many different ways can you arrangethe flower pots?A) 4 B) 24 C) 256 D) 16