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.