PERMUTATIONS
CYNTHIA E. RIO, MAED
PLEASE STAND EVERYONE FOR A PRAYER.
KINDLY PICK UP PIECES OF PAPER
UNDER YOUR CHAIRS AND ARRANGE IT
PROPERLY.
CHECKING OF ATTENDANCE
REVIEW
ARRANGE ME
ARRANGE THE CARDS ACCORDING TO THEIR SUITS IN
ASCENDING ORDER FROM ACE TO KING.
HOW MANY TYPES OR SUITS ARE THERE IN A DECK OF
CARDS?
WHAT ARE THOSE SUITS?
PERMUTATIONS
OBJECTIVES:
1. SOLVE PERMUTATIONS USING THE FORMULA FOR
FINDING THE N OBJECT TAKEN R AT A TIME.
2. SIMPLIFY CIRCULAR PERMUTATIONS AND PERMUTATIONS
WITH REPETITION
3. APPLY PERMUTATIONS IN REAL LIFE SITUATIONS.
PERMUTATIONS

IT IS A SET OF OBJECTS IN AN ORDERED
ARRANGEMENT OF THE OBJECT N.
PERMUTATION FORMULA
• THE PERMUTATION OF N DISTINCT OBJECTS TAKEN ALL AT A TIME IS DEFINED BY
• THE NUMBER OF PERMUTATIONS OF N DISTINCT OBJECT TAKING R ( R≤N ) AT A TIME
WITHOUT REPETITION IS GIVEN BY THE FORMULA
CIRCULAR PERMUTATIONS
• THE NUMBER OF PERMUTATIONS OF N DISTINCT OBJECTS ARRANGED IN A CIRCLE IS GIVEN BY
PERMUTATION WITH REPETITION
• THE NUMBER OF PERMUTATIONS OF N OBJECT WHERE N1 AND N2 ARE ALIKE IS GIVEN BY
DISCUSSION
EXAMPLE 1.
3!
EXAMPLE 2.
THERE ARE 7 PUPILS WHO ENTERED A BUS WITH ONLY 5
EMPTY SEATS AVAILABLE. IN HOW MANY WAYS CAN THESES PUPILS
BE SEATED?
EXAMPLE 3.
IN HOW MANY WAYS CAN A GROUP OF 8 PERSONS
ARRANGE THEMSELVES AROUND A CIRCULAR TABLE?
EXAMPLE 4
HOW MANY DISTINCT PERMUTATIONS CAN BE FORMED
FROMALL THE LETTERS OF THE WORD PARALLEL?
VALUES INTEGRATON
CAN WE APPLY PERMUTATIONS IN REAL-LIFE
SITUATIONS?
APPLICATION
MECHANICS: MAZE ME FRESH
There are 2 groups involved in the activity.
You will be given a maze and solve each
problem in the starting point. Use the
answers as a guide until the end of the
maze. After that, post your work in the board.
This activity is only good for 5 minutes.
DIRECTION
SOLVE EACH EXPRESSION ON PROBLEMS IN
PERMUTATIONS AND THEN HIGHLIGHT THE PATH YOU
TAKE UNTIL THE FINISH POINT. SHOW YOUR
SOLUTIONS IN A GIVEN MANILA PAPER.
EVALUATION
DIRECTIONS: SOLVE THE FOLLOWING PERMUTATIONS. SHOW YOUR SOLUTIONS.
1. FIND THE NUMBER OF PERMUTATIONS OF 8 LETTERS TAKEN 4 AT A TIME.
2. IN HOW MANY WAYS CAN 9 PEOPLE BE SEATED AROUND A CIRCULAR
TABLE?
3. HOW MANY DISTINCT PERMUTATIONS CAN BE FORMED FROM ALL THE
LETTERS OF THE WORD SUCCESS?
ENRICHMENT ACTIVITY
IN HOW MANY WAYS CAN 7 KEYS BE ARRANGED IN A KEY RING?