1. Steve, Michael, John, Lesley are standing in line to buy tickets for a movie. In how many
ways can they stand in line to buy their tickets?
UNDERSTANDING THE PROBLEM
- How many people are standing in line? (four)
- How many ways can they stand in line to buy their ticket? ( did not know)
PLANNING A SOLUTION
Ticket’s counter
S M J L
- Draw a diagram that shows all of them standing in line to
buy a ticket.
- We can look for the arrangement of them when we draw
the diagram.
FINDING THE ANSWER
Draw the diagram
Method 1
S M L J
Method 2
S M J L

2. Method 3
S J M L
Method 4
S J L M
Method 5
S L J M
Method 6
S L M J
Method 7
M S L J
Method 8
M S J L

3. Method 9
M L S J
Method 10
M L J S
Method 11
M J L S
Method 12
M J S L
Method 13
L J M S
Method 14
L J S M
Method 15
L M J S

4. Method 16
L M S J
Method 17
L S M J
Method 18
L S J M
Method 19
J S M L
Method 20
J S L M
Method 21
J M S L
Method 22
J M L S

5. Method 23
J L M S
Method 24
J L S M
LOOKING BACKWARD
When I want to check even the answer is correct or wrong, I used the permutation
formula to solve this question. Therefore,
4
P4= 24
The answer is same even we use the Polya’s model that practice ours to find the
answer step by step.

6. Steve, Michael, John, Lesley are standing in line to buy tickets for a movie. In how many
ways can they stand in line to buy their tickets?
UNDERSTANDING THE PROBLEM
- How many people are standing in line? (four)
- How many ways can they stand in line to buy their ticket? ( did not know)
PLANNING A SOLUTION
- Make a table to look at the arrangement of them without any repetition.
- First person must be at the same places for six times. It means that, the other
three people will exchange themselves.
- Make sure all of them get the chance to be a first person.
FINDING THE ANSWER
FIRST PERSON SECOND PERSON THIRD PERSON FORTH PERSON
Steve Michael John Lesley
Michael Lesley John
John Michael Lesley
John Lesley Michael
Lesley John Michael
Lesley Michael John
Michael Steve John Lesley
Steve Lesley John
John Steve Lesley
John Lesley Steve
Lesley John Steve
Lesley Steve John

7. John Michael Steve Lesley
Michael Lesley Steve
Steve Michael Lesley
Steve Lesley Michael
Lesley Steve Michael
Lesley Michael Steve
Lesley John Steve Michael
John Michael Steve
Steve John Michael
Steve Michael John
Michael John Steve
Michael Steve John
So that, there are 24 ways can they stand in line to buy the tickets.
LOOKING BACKWARD
When I want to check even the answer is correct or wrong, I used the permutation
formula to solve this question. Therefore,
4
P4= 24
The answer is same even we use the Polya’s model that practice ours to find the
answer step by step.

8. JUSTIFICATION
Make a table is easier than draw the diagram because mistake can be avoided. People
always make the mistake, therefore if usetableto solve the question, probability answer
is correct is more than useddiagram. Students also like a table because it is more
attraction than draw the diagram. Make a table is simple and when we use it, it is easy
to make the analysis of the data. All the information will be showed clearly.
PROBLEM EXTENSION
Fatehana, Syahirah, and Ida are standing in line to pay their food at the café. In how
many ways can they stand in line to buy their tickets?
UNDERSTANDING THE PROBLEMS
- How many people are standing in line? (three)
- How many ways can they stand in line to buy their ticket? ( did not know)
PLANNING A SOLUTION
- Make a table to look at the arrangement of them without any repetition.
- First person must be at the same places for six times. It means that, the other
three people will exchange themselves.
- Make sure all of them get the chance to be a first person.
FINDING THE ANSWER
FIRST PERSON SECOND PERSON THIRD PERSON
So that, there are 6 ways can they stand in line to buy the tickets.

9. LOOKING BACKWARD
When I want to check even the answer is correct or wrong, I used the permutation
formula to solve this question. Therefore,
3
P3 = 6
The answer is same even we use the Polya’s model that practice ours to find the
answer step by step.