Section 4-6
Permutations of a Set
Essential Question



How do you find the number of permutations of a set?



Where you’ll see this:

  Cooking, travel, m...
Vocabulary

1. Permutation:



2. Factorial:



3. n Pr :
Vocabulary

1. Permutation: An arrangement of items in a particular order



2. Factorial:



3. n Pr :
Vocabulary

1. Permutation: An arrangement of items in a particular order
                   ORDER IS IMPORTANT!!!

2. Fac...
Vocabulary

1. Permutation: An arrangement of items in a particular order
                   ORDER IS IMPORTANT!!!

2. Fac...
Vocabulary

1. Permutation: An arrangement of items in a particular order
                   ORDER IS IMPORTANT!!!

2. Fac...
Vocabulary

1. Permutation: An arrangement of items in a particular order
                   ORDER IS IMPORTANT!!!

2. Fac...
Vocabulary

1. Permutation: An arrangement of items in a particular order
                   ORDER IS IMPORTANT!!!

2. Fac...
Example 1
How many 3-digit numbers can be formed from the digits 4, 7, and 9 if no
                     repetitions are al...
Example 1
How many 3-digit numbers can be formed from the digits 4, 7, and 9 if no
                     repetitions are al...
Example 1
How many 3-digit numbers can be formed from the digits 4, 7, and 9 if no
                     repetitions are al...
Example 1
How many 3-digit numbers can be formed from the digits 4, 7, and 9 if no
                     repetitions are al...
Example 1
How many 3-digit numbers can be formed from the digits 4, 7, and 9 if no
                     repetitions are al...
Example 1
How many 3-digit numbers can be formed from the digits 4, 7, and 9 if no
                     repetitions are al...
Example 1
How many 3-digit numbers can be formed from the digits 4, 7, and 9 if no
                     repetitions are al...
Permutation Formula
Permutation Formula



              n!
    n
      Pr =
           (n − r)!
Permutation Formula



                                   n!
                         n
                           Pr =
  ...
Example 2
Four letters are taken two at a time. This is the permutation of finding as
              many two-letter groupi...
Example 2
Four letters are taken two at a time. This is the permutation of finding as
              many two-letter groupi...
Example 2
Four letters are taken two at a time. This is the permutation of finding as
              many two-letter groupi...
Example 2
Four letters are taken two at a time. This is the permutation of finding as
              many two-letter groupi...
Example 2
Four letters are taken two at a time. This is the permutation of finding as
              many two-letter groupi...
Example 2
Four letters are taken two at a time. This is the permutation of finding as
              many two-letter groupi...
Example 2
Four letters are taken two at a time. This is the permutation of finding as
              many two-letter groupi...
Example 2
Four letters are taken two at a time. This is the permutation of finding as
              many two-letter groupi...
Example 2
Four letters are taken two at a time. This is the permutation of finding as
              many two-letter groupi...
Example 2
Four letters are taken two at a time. This is the permutation of finding as
              many two-letter groupi...
Example 3
How many 3-digit numbers can be formed from the digits 4, 5, 6, 7, 8, and
                   9 if no repetitions...
Example 3
How many 3-digit numbers can be formed from the digits 4, 5, 6, 7, 8, and
                   9 if no repetitions...
Example 3
How many 3-digit numbers can be formed from the digits 4, 5, 6, 7, 8, and
                   9 if no repetitions...
Example 3
How many 3-digit numbers can be formed from the digits 4, 5, 6, 7, 8, and
                   9 if no repetitions...
Example 3
How many 3-digit numbers can be formed from the digits 4, 5, 6, 7, 8, and
                   9 if no repetitions...
Example 3
How many 3-digit numbers can be formed from the digits 4, 5, 6, 7, 8, and
                   9 if no repetitions...
Example 3
How many 3-digit numbers can be formed from the digits 4, 5, 6, 7, 8, and
                   9 if no repetitions...
Example 3
How many 3-digit numbers can be formed from the digits 4, 5, 6, 7, 8, and
                   9 if no repetitions...
Understanding Break
         1. What is the short way of writing (6)(5)(4)(3)(2)(1)?


                     2. Is (2!)(3!)...
Understanding Break
         1. What is the short way of writing (6)(5)(4)(3)(2)(1)?
                                     ...
Understanding Break
         1. What is the short way of writing (6)(5)(4)(3)(2)(1)?
                                     ...
Understanding Break
         1. What is the short way of writing (6)(5)(4)(3)(2)(1)?
                                     ...
Understanding Break
         1. What is the short way of writing (6)(5)(4)(3)(2)(1)?
                                     ...
Understanding Break
         1. What is the short way of writing (6)(5)(4)(3)(2)(1)?
                                     ...
Homework
Homework




                      p. 174 #1-25 odd




"The inner fire is the most important thing mankind possesses."
  ...
Upcoming SlideShare
Loading in...5
×

Integrated Math 2 Section 4-6

691

Published on

Permutations of a Set

Published in: Education
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
691
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
16
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide







































  • Integrated Math 2 Section 4-6

    1. 1. Section 4-6 Permutations of a Set
    2. 2. Essential Question How do you find the number of permutations of a set? Where you’ll see this: Cooking, travel, music, sports, games
    3. 3. Vocabulary 1. Permutation: 2. Factorial: 3. n Pr :
    4. 4. Vocabulary 1. Permutation: An arrangement of items in a particular order 2. Factorial: 3. n Pr :
    5. 5. Vocabulary 1. Permutation: An arrangement of items in a particular order ORDER IS IMPORTANT!!! 2. Factorial: 3. n Pr :
    6. 6. Vocabulary 1. Permutation: An arrangement of items in a particular order ORDER IS IMPORTANT!!! 2. Factorial: The number of permutations of n items: n(n - 1)(n - 2)... (3)(2)(1) 3. n Pr :
    7. 7. Vocabulary 1. Permutation: An arrangement of items in a particular order ORDER IS IMPORTANT!!! 2. Factorial: The number of permutations of n items: n(n - 1)(n - 2)... (3)(2)(1) 5! = (5)(4)(3)(2)(1) 3. n Pr :
    8. 8. Vocabulary 1. Permutation: An arrangement of items in a particular order ORDER IS IMPORTANT!!! 2. Factorial: The number of permutations of n items: n(n - 1)(n - 2)... (3)(2)(1) 5! = (5)(4)(3)(2)(1) = 120 3. n Pr :
    9. 9. Vocabulary 1. Permutation: An arrangement of items in a particular order ORDER IS IMPORTANT!!! 2. Factorial: The number of permutations of n items: n(n - 1)(n - 2)... (3)(2)(1) 5! = (5)(4)(3)(2)(1) = 120 3. n Pr : n permutations taken r at a time; n is the number of different items and r is the number of items taken at a time
    10. 10. Example 1 How many 3-digit numbers can be formed from the digits 4, 7, and 9 if no repetitions are allowed?
    11. 11. Example 1 How many 3-digit numbers can be formed from the digits 4, 7, and 9 if no repetitions are allowed?
    12. 12. Example 1 How many 3-digit numbers can be formed from the digits 4, 7, and 9 if no repetitions are allowed? 3
    13. 13. Example 1 How many 3-digit numbers can be formed from the digits 4, 7, and 9 if no repetitions are allowed? 3 2
    14. 14. Example 1 How many 3-digit numbers can be formed from the digits 4, 7, and 9 if no repetitions are allowed? 3 2 1
    15. 15. Example 1 How many 3-digit numbers can be formed from the digits 4, 7, and 9 if no repetitions are allowed? 3 2 1 (3)(2)(1)
    16. 16. Example 1 How many 3-digit numbers can be formed from the digits 4, 7, and 9 if no repetitions are allowed? 3 2 1 (3)(2)(1) = 6 numbers
    17. 17. Permutation Formula
    18. 18. Permutation Formula n! n Pr = (n − r)!
    19. 19. Permutation Formula n! n Pr = (n − r)! n is the number of different items and r is the number of items taken at a time
    20. 20. Example 2 Four letters are taken two at a time. This is the permutation of finding as many two-letter groupings of the four letters.
    21. 21. Example 2 Four letters are taken two at a time. This is the permutation of finding as many two-letter groupings of the four letters. n! P= n r (n − r)!
    22. 22. Example 2 Four letters are taken two at a time. This is the permutation of finding as many two-letter groupings of the four letters. n! P= n r (n − r)! 4 P2
    23. 23. Example 2 Four letters are taken two at a time. This is the permutation of finding as many two-letter groupings of the four letters. n! P= n r (n − r)! 4! P = 4 2 (4 − 2)!
    24. 24. Example 2 Four letters are taken two at a time. This is the permutation of finding as many two-letter groupings of the four letters. n! P= n r (n − r)! 4! 4! P = 4 2 = (4 − 2)! 2!
    25. 25. Example 2 Four letters are taken two at a time. This is the permutation of finding as many two-letter groupings of the four letters. n! P= n r (n − r)! 4! 4! (4)(3)(2)(1) P = 4 2 = = (4 − 2)! 2! (2)(1)
    26. 26. Example 2 Four letters are taken two at a time. This is the permutation of finding as many two-letter groupings of the four letters. n! P= n r (n − r)! 4! 4! (4)(3)(2)(1) P = 4 2 = = (4 − 2)! 2! (2)(1)
    27. 27. Example 2 Four letters are taken two at a time. This is the permutation of finding as many two-letter groupings of the four letters. n! P= n r (n − r)! 4! 4! (4)(3)(2)(1) P = 4 2 = = (4 − 2)! 2! (2)(1)
    28. 28. Example 2 Four letters are taken two at a time. This is the permutation of finding as many two-letter groupings of the four letters. n! P= n r (n − r)! 4! 4! (4)(3)(2)(1) P = 4 2 = = =12 (4 − 2)! 2! (2)(1)
    29. 29. Example 2 Four letters are taken two at a time. This is the permutation of finding as many two-letter groupings of the four letters. n! P= n r (n − r)! 4! 4! (4)(3)(2)(1) P = 4 2 = = =12 (4 − 2)! 2! (2)(1) 12 two-letter groupings can be made
    30. 30. Example 3 How many 3-digit numbers can be formed from the digits 4, 5, 6, 7, 8, and 9 if no repetitions are allowed?
    31. 31. Example 3 How many 3-digit numbers can be formed from the digits 4, 5, 6, 7, 8, and 9 if no repetitions are allowed? n! P= n r (n − r)!
    32. 32. Example 3 How many 3-digit numbers can be formed from the digits 4, 5, 6, 7, 8, and 9 if no repetitions are allowed? n! P= n r (n − r)! 6 P3
    33. 33. Example 3 How many 3-digit numbers can be formed from the digits 4, 5, 6, 7, 8, and 9 if no repetitions are allowed? n! P= n r (n − r)! 6! P = 6 3 (6−3)!
    34. 34. Example 3 How many 3-digit numbers can be formed from the digits 4, 5, 6, 7, 8, and 9 if no repetitions are allowed? n! P= n r (n − r)! 6! 6! P = 6 3 = (6−3)! 3!
    35. 35. Example 3 How many 3-digit numbers can be formed from the digits 4, 5, 6, 7, 8, and 9 if no repetitions are allowed? n! P= n r (n − r)! 6! 6! P = 6 3 = = (6)(5)(4) (6−3)! 3!
    36. 36. Example 3 How many 3-digit numbers can be formed from the digits 4, 5, 6, 7, 8, and 9 if no repetitions are allowed? n! P= n r (n − r)! 6! 6! P = 6 3 = = (6)(5)(4) =120 (6−3)! 3!
    37. 37. Example 3 How many 3-digit numbers can be formed from the digits 4, 5, 6, 7, 8, and 9 if no repetitions are allowed? n! P= n r (n − r)! 6! 6! P = 6 3 = = (6)(5)(4) =120 (6−3)! 3! 120 3-digit number can be formed
    38. 38. Understanding Break 1. What is the short way of writing (6)(5)(4)(3)(2)(1)? 2. Is (2!)(3!) the same as 6! ? 3. Which of the following is the value of 0! ? a. 0 b. 1 c. -1 d. ±1 4. Which of the following are examples of permutations? a. Arranging 5 people on a bench that seats 5 b. Choosing 4 letters from 6 and writing all possible arrangements of the choices c. Selecting a committee of 3 from 10 women
    39. 39. Understanding Break 1. What is the short way of writing (6)(5)(4)(3)(2)(1)? 6! 2. Is (2!)(3!) the same as 6! ? 3. Which of the following is the value of 0! ? a. 0 b. 1 c. -1 d. ±1 4. Which of the following are examples of permutations? a. Arranging 5 people on a bench that seats 5 b. Choosing 4 letters from 6 and writing all possible arrangements of the choices c. Selecting a committee of 3 from 10 women
    40. 40. Understanding Break 1. What is the short way of writing (6)(5)(4)(3)(2)(1)? 6! 2. Is (2!)(3!) the same as 6! ? No; (2)(1)(3)(2)(1) ≠ (6)(5)(4)(3)(2)(1) 3. Which of the following is the value of 0! ? a. 0 b. 1 c. -1 d. ±1 4. Which of the following are examples of permutations? a. Arranging 5 people on a bench that seats 5 b. Choosing 4 letters from 6 and writing all possible arrangements of the choices c. Selecting a committee of 3 from 10 women
    41. 41. Understanding Break 1. What is the short way of writing (6)(5)(4)(3)(2)(1)? 6! 2. Is (2!)(3!) the same as 6! ? No; (2)(1)(3)(2)(1) ≠ (6)(5)(4)(3)(2)(1) 3. Which of the following is the value of 0! ? a. 0 b. 1 c. -1 d. ±1 4. Which of the following are examples of permutations? a. Arranging 5 people on a bench that seats 5 b. Choosing 4 letters from 6 and writing all possible arrangements of the choices c. Selecting a committee of 3 from 10 women
    42. 42. Understanding Break 1. What is the short way of writing (6)(5)(4)(3)(2)(1)? 6! 2. Is (2!)(3!) the same as 6! ? No; (2)(1)(3)(2)(1) ≠ (6)(5)(4)(3)(2)(1) 3. Which of the following is the value of 0! ? a. 0 b. 1 c. -1 d. ±1 4. Which of the following are examples of permutations? a. Arranging 5 people on a bench that seats 5 b. Choosing 4 letters from 6 and writing all possible arrangements of the choices c. Selecting a committee of 3 from 10 women
    43. 43. Understanding Break 1. What is the short way of writing (6)(5)(4)(3)(2)(1)? 6! 2. Is (2!)(3!) the same as 6! ? No; (2)(1)(3)(2)(1) ≠ (6)(5)(4)(3)(2)(1) 3. Which of the following is the value of 0! ? a. 0 b. 1 c. -1 d. ±1 4. Which of the following are examples of permutations? a. Arranging 5 people on a bench that seats 5 b. Choosing 4 letters from 6 and writing all possible arrangements of the choices c. Selecting a committee of 3 from 10 women
    44. 44. Homework
    45. 45. Homework p. 174 #1-25 odd "The inner fire is the most important thing mankind possesses." - Edith Sodergran
    1. A particular slide catching your eye?

      Clipping is a handy way to collect important slides you want to go back to later.

    ×