Answered: What is the number of possible…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Direction: Analyze and solve the following problems. 1. What is the number of possible arrangements of 9 books on a shelf where 4 are of the same kind, 3 are of the same kind, and 2 are of the same kind? 2. In how many ways can 3 rhinestones, 5 crystals, and 2 precious metals be arranged into a bracelet? 3. Find the number of distinguishable permutations of the digits of the number 811 812 271 4. How many different arrangements are possible for 10 cars in a line, if 2 are red, 3 are black, and 5 are white. 5. What is the number of possible arrangements of 10 shirts on a shelf where 4 are of the same kind, 3 are of the same kind, and 2 are of the same kind? 6. Find the number of circular permutations of 8 children. 7. In how many different ways can a class of 10 sit around a table if they may sit in any way? 8. How many ways can 8 people be seated at a square table? 9. Six people are going to sit at a round table. How many different ways can this be done? 10. A couple wants to plant some shrubs around a circular walkway. They have seven different shrubs. How many ways can the shrubs be planted? 11. There are nine keys on a standard key ring with no clasp. How manu different arrangements are there? 12. 4 boys and 4 girls are seated alternatively at a round table. If a girl must be seated first, how many ways can you seat the boys and girls? 13. How many ways can 5 different keys be arranged on a key ring? 4-5. in a playground, 3 sisters and 8 other girls are playing together. In a particular game, how many ways can all the girl be seated in a circular order so that the three sisters are not seated together? --------------- REFLECTION: (Journal writing) In your journal notebook, reflect and answer the questions. How can we determine the distinguishable objects? In your own opinion, if your father is both beneficiary of the Government Amelioration Program and Supplemental SAP, what do you think the effect of this to you.

ot distinguisn amorag thes2 four arrangeroents unless one of the obje s.
S u nose we fax gu est A as shovwn. "Dhen we arrange the thrse other 2
There are 6 circular permutations for the guests. Note that 4 permutations for the 4 guests
were indistinguishable. The results lead to this theorem.
The number of circular permutations of n objects is
n!
or (n- 1)!
There is a special case of permutation where the arrangement of things is in a circular pattern. It is
called circular permutation. The most common example of this type is the seating arrangement of
people around a circular table.
When people are seated around a circular table, we cannot say that one is seated on the first seat
unlike what we have seen on linear permutations (arrangement of things in a line).
Ilustrative Example 1:
Find the number of circular permutations of seven dancers.
%3D
(n– 1)! = (7– 1)! = 6! = 720
There are 720 circular permutations.
Vhat if we consider the direction of the arrangement in clockwise or in the counter- clockwise
í difforent heads in a bracelet, keys on the key rings, and

REFLECTION: (Journal Writing)
In your journal notebook, reflect and answer the questions.
How. can we determine the distinguishable objects? In your own opinion, if your father is both
beneficiary of the Government Amelioration Program and Supplemental SAP, what do you think the effect
of this to you.
REFERENCES:
Grade 10 Mathematics Pattern and Practicalities by Gladys C, Nivera, Ph.d and Mini Rose
C. Lapinid, Ph.D.
CIRCULAR PERMUTATION
Lesson
Explore
The King has to arrange four guests A, B, C, and D around a circalar
table, What are the possible arrangements?
s vou distinguÍsh armoTng these four arrangenments?
B, C, D, A
D, A, B,C
1 C, D.A, B
A, B, C,D

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