Circular permutation

REVIEW

•HOW MANY DISTINGUISHABLE PERMUTATIONS ARE POSSIBLE WITH ALL THE LETTERS OF THE WORD

“ELLIPSES”

CIRCULAR PERMUTATION

AARON JAMES D. LICOMATH TEACHER

LETS THINK !!!!

IN HOW MANY WAYS CAN 3 STUDENTS SEATED IN A CIRCULAR/ROUND TABLE?

In how many ways can 3 students seated in a circular/round table?

1st arrangement

2nd arrangement

THERE ARE 2 POSSIBLE ARRANGEMENT.ANSWER:

ACTIVITY # 1

IN HOW MANY WAYS CAN 2 BOYS AND 1 GIRL CAN BE SEATED AROUND A TABLE?

IN HOW MANY WAYS CAN 2 BOYS AND 1 GIRL CAN BE SEATED AROUND A TABLE?

THERE ARE 3 PERSONS INVOLVED

1st arrangement2nd arrangement

THERE ARE 2 POSSIBLE ARRANGEMENT.ANSWER:

IN HOW MANY WAYS CAN 4 PEOPLE BE SEATED AROUND A CIRCULAR TABLE?

ACTIVITY # 2

THEREFORE THERE ARE 6 WAYS TO SEAT 4 PEOPLE IN A CIRCULAR TABLE.

WHAT PROCESS/SOLUTION DID YOU USED FOR YOU TO GET THE ANSWER?

DO YOU THINK WE CAN EASILY GET THE ANSWER WITHOUT LISTING THE POSSIBLE ARRANGEMENT?

HOW?

THE PERMUTATION OF N OBJECTS ARRANGED IN A CIRCLE IS :

P = (N – 1)!

WHEN DO WE USE CIRCULAR PERMUTATION?

WHAT PARTICULAR SCENARIO OR SITUATION

CAN THIS BE DONE?

EXAMPLE

CALCULATE THE CIRCULAR PERMUTATIONS OF 7 ELEMENTS.P= (7 − 1)!P = 6!P = 6 · 5 · 4 · 3 · 2 · 1P = 720

HOW MANY WAYS CAN EIGHT PEOPLE SIT AROUND A ROUND TABLE?

P = (8 – 1) !P = 7!P = 7 * 6 * 5 * 4 * 3 * 2 * 1P= 5,040

SEAT WORK

1. IN HOW MANY WAYS CAN 8 PERSONS SEATED IN A CIRCULAR TABLE?

2. FIND THE NUMBER OF WAYS IN WHICH 5 PEOPLE A,B,C,D,E CAN BE SEATED AT A ROUND TABLE?

ASSIGNMENT

FIND THE NUMBER OF DIFFERENT WAYS THAT A FAMILY 0F 6 CAN BE SEATED AROUND A CIRCULAR TABLE WITH 6 CHAIRS.