CYCLIC PERMUTATION.pptx

PERMUTATION

1. CYCLIC PERMUTATION

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:      

3. The number of permutation of n different things around a key ring and the like is:      

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? c. In how many ways can she do it if Grumpy and Dopey must not 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?

9. EVALUATION

10. Direction: Solve each problem. Show your solution. 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; c. If the eldest and the youngest sit side by side?

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 and four children stand in a circle. In how many ways can they arrange themselves if mother and father stand opposite each other? 2. Try to explore – give at least 5 application of PERMUTATION. (Any type of permutation)

14. Had a wonderful Day ahead.