pre-cal 40s slides november 28, 2007
DESCRIPTION
Circular permutations.TRANSCRIPT
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Circular Permutations
Circle of life
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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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(6 - 1)! = 5! 2 2 = 60
Example: How many bracelets can can be made from 6 different beads?
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:
(6 - 1)! = 5! = 120
Example: How many different ways can 6 people be seated around a circular table?
(n - 1)!
The number of ordered arrangements that can be made of n objects in a circle is given by:
Circular Permutations
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How many distinguishable ways can 3 beads be arranged on a circular bracelet?
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How many distinguishable ways can 4 beads be arranged on a circular bracelet?
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(b) men and women alternate?(a) spouses sit opposite each other?
In how many ways can 4 married couples seat themselves around a circular table if: