Permutations of Non-
Distinguishable Objects
          and
Circular Permutations




Poker fun with your best friends by fl...
How many four-digit even numbers are there if the same digit cannot
be used twice?
How many four-digit even numbers are there if the same digit can be
repeated?
In how many ways can 8 books be arranged on a shelf, if 3 particular
books must be together?
How many different 4 letter quot;wordsquot; can you make from the
letters in the word BOOK?
K O OB
B O OK
BOOK     KOOB
BO K O   K O BO
BO K O   K O BO
Permutations of Non-
Distinguishable Objects

 The number of ways to arrange n objects that contain
 sets of non-distingui...
Example: How many different quot;wordsquot; can be made form the
letters in the word:

    (a) BOOK                       ...
How many different quot;wordsquot; can you make from the letters
in the word STATISTICS?
How many distinguishable ways can 3 people be seated
around a circular table?
How many distinguishable ways can 4 people be seated
around a circular table?
Circular Permutations

 The number of ordered arrangements that can be made of n
 objects in a circle is given by:



    ...
How many distinguishable ways can 3 beads be
arranged on a circular bracelet?
Circular Permutations


  Special Case: A bracelet is a circle that can be flipped over.
  The number of different arrangem...
How many distinguishable ways can 4 beads be
arranged on a circular bracelet?
Pre-Cal 40S May 6, 2009
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Pre-Cal 40S May 6, 2009

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Permutations of Non-Distinguishable Objects and Circular Permutations.

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Transcript of "Pre-Cal 40S May 6, 2009"

  1. 1. Permutations of Non- Distinguishable Objects and Circular Permutations Poker fun with your best friends by flickr user coltfan909
  2. 2. How many four-digit even numbers are there if the same digit cannot be used twice?
  3. 3. How many four-digit even numbers are there if the same digit can be repeated?
  4. 4. In how many ways can 8 books be arranged on a shelf, if 3 particular books must be together?
  5. 5. How many different 4 letter quot;wordsquot; can you make from the letters in the word BOOK?
  6. 6. K O OB B O OK BOOK KOOB BO K O K O BO BO K O K O BO
  7. 7. Permutations of Non- Distinguishable Objects The number of ways to arrange n objects that contain sets of non-distinguishable objects is given by:
  8. 8. Example: How many different quot;wordsquot; can be made form the letters in the word: (a) BOOK (b) MISSISSIPPI # of O's = 2 ∴ # of I's = 4 # of S's = 4 # of P's = 2 ∴
  9. 9. How many different quot;wordsquot; can you make from the letters in the word STATISTICS?
  10. 10. How many distinguishable ways can 3 people be seated around a circular table?
  11. 11. How many distinguishable ways can 4 people be seated around a circular table?
  12. 12. Circular Permutations The number of ordered arrangements that can be made of n objects in a circle is given by: (n - 1)! Example: How many different ways can 6 people be seated around a circular table? (6 - 1)! = 5! = 120
  13. 13. How many distinguishable ways can 3 beads be arranged on a circular bracelet?
  14. 14. Circular Permutations Special Case: A bracelet is a circle that can be flipped over. The number of different arrangements that can be made of objects on a bracelet is: Example: How many bracelets can can be made from 6 different beads? (6 - 1)! = 5! 2 2 = 60
  15. 15. How many distinguishable ways can 4 beads be arranged on a circular bracelet?

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