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Hay Naku
1.
CIRCULAR PERMUTATION
2.
Hello folks this is Precious your scribe for today. Today Mr. K introduced to us the Circular Permutation. What is Circular permutation? Circular Permutation is the number of ordered arrangements that can be made of n objects in a circle is given by: ( n ‐ 1 ) ! and in special problems like bracelets and necklaces that can flip over we can use: ( n ‐ 1 ) !
2
3.
Example number 1: How many distinguishable ways can 3 people be seated around a
circular table? hint: **person 3 is our point of reference Solution: ( n 1 ) ! ( 3 1 ) ! 2! person 3 2 x 1 person 2 person 1 2 person 3 person 1 person 2 therefore there are 2 ways to seat 3 people in a circular table.
4.
Example number 2: How many distinguishable ways can 4 people be seated around a circular table?
hint: quot;Aquot; is our point of reference Solution: A A A ( n 1)! B D D C C D ( 4 1)! 3! B B C 3 x 2 x 1 A A A 6 B D B C B C threrefore there are 6 ways to seat 4 people C D D in a circular table
5.
Example number 3: How many distinguishable ways can 4 beads be arranged on a circular bracelet? Solution:
( n 1)! 2 bead 1 ( 4 1 )! bead 1 2 3! bead 4 bead 2 bead 3 2 bead 4 3 x 2 x 1 bead 3 bead 2 2 6 bead 1 2 3 bead 2 bead 3 hint: bead 1 is our point of bead 4 reference
6.
And then Mr. K decides to form us into groups to solve this problem: In how many ways can 4 married couples seat themselves around a circular table if: a.) spouses sit opposite each other?
Solution: ( n 1 )! **here we have our formula then we ( 4 1 )! know that there is 4 spouses subtract 1 3! and then factorial. 3 x 2 x 1 6
7.
b.) men and women alternate? Solution:
ladies x men ( 4 1 )! x 4! 3! x 4! lady 1 6 x 24 4 choices of men 1 choice of man 144 ways to seat a men and a lady 2 lady 4 women alternate on a circular table 2 choices of men 3 choices of men lady 3
8.
The next scribe is Mary Ann......
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