Pre-Cal 40S May 6, 2009
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Transcript of Pre-Cal 40S May 6, 2009
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Permutations of Non-Distinguishable Objects
andCircular Permutations
Poker fun with your best friends by flickr user coltfan909
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How many four-digit even numbers are there if the same digit cannot be used twice?
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How many four-digit even numbers are there if the same digit can be repeated?
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In how many ways can 8 books be arranged on a shelf, if 3 particular books must be together?
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How many different 4 letter "words" can you make from the letters in the word BOOK?
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B KOOB OO KBO K OBOK O
KO OBK O O BK O BOK OBO
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Permutations of Non-Distinguishable Objects
The number of ways to arrange n objects that containsets of non-distinguishable objects is given by:
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Example: How many different "words" can be made form the letters in the word:
# of O's = 2 ∴
# of I's = 4 # of S's = 4 # of P's = 2 ∴
(a) BOOK (b) MISSISSIPPI
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How many different "words" can you make from the letters in the word STATISTICS?
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How many distinguishable ways can 3 people be seated around a circular table?
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How many distinguishable ways can 4 people be seated around a circular table?
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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
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How many distinguishable ways can 3 beads be arranged on a circular bracelet?
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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
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How many distinguishable ways can 4 beads be arranged on a circular bracelet?