mathematics 10

1. Fundamental
Counting Principle
THIRD QUARTER MATHEMATICS 10
ISAAC M. SUBELDIA
Mathematics Teacher

2. Priming : Rock, Paper, Scissors

3. OBJECTIVES:
• Identify the fundamental counting principle
(FCP).
• Answer exercises applying FCP.
• Solves problems involving FCP.

4. LIST ALL THE POSSIBLE OUTCOME OF
THE GAME ROCK, PAPER, SCISSOR
Rock - Rock Rock - Paper Rock - Scissor
Paper – Paper Paper – Scissor Paper - Rock
Scissor – Scissor Scissor – Rock Scissor – Paper
9 possible outcome.

7. Together with your partner answer the following problems:
Present your answer to the class.
Problem 1
Victoria invited Nina to her birthday
party. Nina has 4 new blouses (stripes, with
ruffles, long-sleeved, and sleeveless) and
3 skirts (red, pink, and black) in her closet
reserved for such occasions.
• Assuming that any skirt can be paired with any blouse, in how many
ways can Nina select her outfit? List the possibilities.
• How many blouse-and-skirt pairs are possible?
• Show the other way of finding the answer in item 1.

8. 3. What can you say about the list you made?
Problem 2
Suppose Daniel secured his bike using
combination lock. Later he realized that he
forgot the 4-digit code. He only remembered
that the code contains the digits 1, 3, 4, and 7.
• List all the possible codes out of the given digits.
• How many possible codes are there?
• What can you say about the list you made?

9. Our canteen regularly prepares your
snacks. This is also one source of our
fund to support the need of our school.
A meal consists of a bread, hot soup and
beverage. How many different set of
snack can be selected if there are 2
bread (Hamburger, Egg burger), 3 hot
soup (sopas, sampurado, aruzcaldo) and
2 beverages (juice, mineral water)
available?

10. Solution:
2 Bread x 3 soup x 2
beverages= 12 sets

11. The Fundamental Counting Principle states
that if one event can occur m ways and a
second event can occur n ways, the
number of ways the two events can
occur in sequence is m • n.

12. How many possible outcomes if you
toss to coins?

15. Developing Mastery:

16. Answers.
1. 3 x 2 x 1 = 6
2. 2 x 5 x 3 = 30
3. 4 x 4 x 4 x 4 x 4 = 1024

17. Application
How many ways can you choose 6
numbers in a LOTTO?
USING FPC
75 x 74 x 73 x 72 x 71 x 70
= 144, 978, 876, 000

18. GENERALIZATION
Fundamental Counting Principle – states
that if activity A can be done in n1 ways,
activity B can be done in n2 ways, activity
C in n3 ways, and so on, then activities
A, B, and C can done simultaneously
n1*n2*n….ways
DID WE MEET OUR OBJECTIVES?

19. Evaluation
Direction: Choose the letter of the
correct answer 1 minute each
question.

20. EVALUATION: Project 555
Direction: Read the problem carefully then
choose the letter of the correct answer:
2 minutes each problem.
Are you ready?

21. 1. Ben can take any one of three routes from school (S)
to the town center (T), and can then take five possible
routes from the town center to his home (H). He doesn't
retrace his steps.
How many different possible ways can Ben walk home
from school?
a. 7 b. 8
c. 15 d. 56

22. 2.Sarah goes to her local pizza parlor and orders a pizza.
She can choose either a large or a medium pizza, has a
choice of seven different toppings, and can have three
different choices of crust.
How many different pizzas could Sarah order?
a. 12 b. 20
c. 27 d. 42

23. 3.Derek must choose a four-digit PIN number. Each
digit can be chosen from 0 to 9. How many different
possible PIN numbers can Derek choose? d
a. 5,040 b. 6,541
c. 9,000 d. 10,000

24. 4.Jenny has nine different skirts, seven
different tops, ten different pairs of shoes, two
different necklaces and five different
bracelets. In how many ways can Jenny dress
up?
a. 6,300 b. 7,560
c. 12, 600 d. 63,000

25. 5.A meal consists of a main dish, a side dish, and a dessert.
How many different meals can be selected if there are 3
main dishes, 3 side dishes and 7 desserts available?
a. 40 b. 63
c. 21 d. 27

26. Answer:
1. C
2. D
3. D
4. A
5. B

27. HOME WORK
Prepare one problem involving
Fundamental Principle of
Counting with answer and
solution.