This document discusses cyclic permutation and provides examples of solving cyclic permutation problems. It defines cyclic permutation as arranging distinct objects around a fixed circle. The number of permutations when arranging n distinct objects in a circle is (n-1)!. It also provides the formula for arranging objects on a key ring or bracelet as (n-1)!/2. The document gives several examples of solving cyclic permutation problems and directs the reader to solve additional problems showing their work.

2. Cyclic Permutation
The number of ways to arrange
distinct objects along a fixed circle is.
If n objects are to be arranged around a
circle, the number of permutation of n
different things is:
(𝒏 − 𝟏)! = (𝒏 − 𝟏)(𝒏 − 𝟐)(𝒏 − 𝟑) … (𝟐)(𝟏)

3. The number of permutation of n different
things around a key ring and the like is:
𝒏 − 𝟏 !
𝟐
=
𝒏 − 𝟏 𝒏 − 𝟐 𝒏 − 𝟑 … (𝟐)(𝟏)
𝟐

4. Examples:
Direction: Solve each problem.
1. In how many ways can 7 people be seated it
at
round table?
2. Snow white arranges the seven dwarfs
around a
May-pole.
a. How many ways can she arrange
them?
b. In how many ways can she do it if Doc
&
Sleepy are to be together?

5. Examples:
3. In how many ways can 7 keys be
arranged in a
key ring?
4. In how many ways may the vertices of a
regular heptagon be named with the
letters
A, B, C,, D, E, F, and G?
5. In how many ways can nine different
colored
beads be arranged on a bracelet?

6. Do as directed.
1. In how many ways can six boys and
six girls be seated at a round table if:
a. They may be seated anywhere
b. If the couples (Boy and Girl) will
be seated together
c. If the boys will be seated next to
each other.

7. Do as directed.
2. A spinner is divided in 5 equal parts,
how many ways can you arrange 5
colors in it?
3. At one stage in the court of Camelot.
King Arthur and 12 knights would be
seat at the round table. If each person
could sit anywhere how many different
arrangements were possible?

8. • What is CYCLIC PERMUTATION?
• What are the formulas/ formulae in solving
CYCLIC PERMUTATION?

10. Direction: Solve each problem. Show your
solution.
1. In how many ways can 10
different
colored toy horses be arranged
in a merry-go-round?
2. In how many ways can 10
different colored beads be
made into a bracelet?

11. Direction: Solve each problem. Show your
solution.
3. In how many ways can eight keys be
arranged on a key ring?
4. In how many ways can seven
children be
seated at a round table if:
a. They may be seated anywhere;
b. If the eldest will be seated on the
right
side of the youngest;

12. Direction: Solve each problem. Show your
solution.
5. In how many ways can 7
students be seated in round table,
if two particular students must not
be seated next to each other?

13. ASSIGNMENT
1. Mother, father andfour children standin a circle. In
how many ways can they arrange themselves if mother
andfather stand opposite each other?
2. Try to explore – give at least 5 application of
PERMUTATION. (Any type of permutation)