Math 10

1. Math 10
Permutation

2. Quarter 3 Week 1
OBJECTIVES:
illustrate the permutation of objects (M10SP-IIIa-1)
solve problems involving permutations (M10SP-
IIIb-1).

3. Quarter 3 Week 1
OBJECTIVES:
•discuss the fundamental counting principle (FCP)
in determining the number of possibilities in a
certain event
•solve events using the fundamental counting
principle (FCP)

4. Quarter 3 Week 1
OBJECTIVES:
•construct the tree diagram clearly
•display perseverance while doing the task
•show concern for others

5. Observe
DO RE MI
A B C
1 2 3

6. What did you notice?
DO RE MI
A B C
1 2 3
Arrangement
or Order

7. Recall
The Fundamental Counting Principle states
that if there are p ways to choose one
thing, and q ways to choose another thing,
then there are p x q ways to do both
things. Thus, this follows the multiplication
rule.

8. Example:
• Matchy-matchy!
Andrea has 4 new blouses (stripes, with ruffles,
long-sleeved, and sleeveless) and 3 skirts (black,
red, and pink) ready for all occasions.

9. Solution
From the given, there are 4 blouses
and 3 skirts.
Let us assign: p = 4 and q = 3

10. Solution
Using the Fundamental Counting
Principle, we multiply p and q to
answer the given:
p x q = 4 x 3 = 12 ways

11. The 12 ways are:

12. • In English “!” is known as an
exclamation point, used to
express strong emotion. In
Filipino “!” it is read as
“Tandang Padamdam”. In
mathematics, the symbol
represents the factorial
operation.
• “!” IS READ AS
FACTORIAL
Exclamation point

13. Remember that:
Mathematicians use an exclamation
point after n to indicate the product
by writing n!.
The exclamation point is the factorial
symbol, and n! is read as
“n factorial”.

14. Examples:
•4! = 4•3•2•1 = 24
•3! = 3•2•1 = 6
•2! = 2•1 = 2
•1! = 1
•0! = 1 (0! is identified as 1,
which is a neutral element
in multiplication)

15. What is PERMUTATION?
Permutation refers to the different
possible arrangement of a set of
objects where order matters. There
are different ways in which a
collection of items can be arranged.

16. Example:
There are different ways in which the letters
A, B and C can be arranged together, taken
all at a time, are ABC, ACB, BCA, CBA, CAB,
and BAC. Note that ABC and CBA are
different arrangement in terms of order.

17. Try this!
A Plantita intends to display her 5
distinct potted plants and wishes to
arrange 3 of them in a row. In how
many ways can this be done?

18. Solution:
The permutation of 5 potted plants
taken 3 at a time is represented by 𝑃
(5,3), 5𝑃3 , or 𝑃5,3

19. Solution:
The equation for permutation of n objects
taken r at a time:
Note that, n is the number of objects and
r is the number of objects
taken at a time (factors)
𝑷(𝒏,𝒓)=
𝑛!
𝑛−𝑟 !
, 𝒏≥𝒓

20. GIVEN n = 5, r = 3:
𝑷(𝒏,𝒓)=
𝑛!
𝑛−𝑟 !
, 𝒏≥𝒓
𝑷(𝒏,𝒓)=
5!
5−3 !
𝑷(𝒏,𝒓)=
5𝑥4𝑥3𝑥2𝑥1
2!
=
5𝑥4𝑥3𝑥2𝑥1
2𝑥1
= 5𝑥4𝑥3
𝑷(𝒏,𝒓) = 5𝑥4𝑥3 = 60
𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑤𝑎𝑦𝑠

21. Another Example!
Suppose there were 8 runners in a 500m
race. In how many ways can the first 3
places (First, Second, and Third) be filled?

22. GIVEN n = 8, r = 3:
𝑷(𝒏,𝒓)=
𝑛!
𝑛−𝑟 !
, 𝒏≥𝒓
𝑷(𝒏,𝒓)=
8!
8−3 !
𝑷(𝒏,𝒓)=
8𝑥6𝑥7𝑥5𝑥4𝑥3𝑥2𝑥1
5!
=
8𝑥7𝑥6𝑥5𝑥4𝑥3𝑥2𝑥1
5𝑥4𝑥3𝑥2𝑥1
𝑷(𝒏,𝒓) = 8𝑥7𝑥6 = 336
𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑤𝑎𝑦𝑠

23. Assignment:

24. Observe this!
A photo contest organizer selected 5
photogenic winners. In how many ways can
these 5 winners arrange themselves in a row
for picture taking?

25. GIVEN n = 5, r = 5:
𝑷(𝒏,𝒓)=
𝑛!
𝑛−𝑟 !
, 𝒏≥𝒓
𝑷(𝒏,𝒓)=
5!
5−5 !
𝑷(𝒏,𝒓)= 5! = 5𝑥4𝑥3𝑥2𝑥1
𝑷(𝒏,𝒓) = 120 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑤𝑎𝑦𝑠

26. Concluding Statement:

27. Educational
Technology
Unit
Sir Therence
teacher
Math 10

28. Thank You!
For comments/suggestions contact or e-mail me at
facebook.com/therence.ubas
therence.ubas@deped.gov.ph