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.