Introduction to Permutation

1. Fundamental
Counting Principle
Lesson 1

2. Objectives:
(1) Illustrates the Fundamental Counting
Principle through the tree diagram or by
using the table.
(2) Apply the fundamental principle of
counting to determine the possible
number of ways.

3. REVIEW
An anagram is a type of wordplay, wherein the
results of arranging the letters of a word or
phrase, produce a new word or phrase by using
the original letters exactly once. For example,
the word silent is an anagram of the word
listen.

4. DRILL
Find anagrams of these words. (Hint: body
parts)
A. are _________
B. gel _________
C. ram _________
D. sink_________
E. lamp __________
F. fringe __________
G. earth __________
EAR
LEG
ARM
SKIN
PALM
FINGER
HEART

5. Now were done arranging the
letters of a word to produce
a new word, next we are going
to arrange and identify how
many possible ways we can
make based on the given
situation.

6. Situation 1
1. If you are going on a friendly date this
Valentine’s Day with your crush and you
have three new pairs of pants and three
new tops in your cabinet. In how many ways
can you dress? Make a tree diagram to
show all the choices you can make.

7. Situation 1
Recalling our lessons in the previous grades, we
simply match the three pants to the tops one by
one and counting the results will give the desired
number. We can use the tree diagram so that we
can visualize the results.

8. From the illustration, we can see that there are
nine different ways of matching the pants and the
tops. Thus, there are nine resulting outfits one can
make out of the three different pants and three
different tops.

9. Situation 2
You go to a restaurant to buy some
breakfast. The menu says, for food:
pancakes, waffles, or home fries; and for
drinks coffee, juice, hot chocolate, and
tea. How many different choices of food
and drink do you have? Illustrate the
choices by using table below.
Food/Drinks Coffee
(C)
Juice
(J)
Hot Chocolate
(H)
Tea
(T)
Pancake (P)
Waffles (W)
Fries (F)

10. Food/Drinks Coffee
(C)
Juice
(J)
Hot
Chocolate
(H)
Tea
(T)
Pancake (P)
Waffles (W)
Fries (F)
PC PJ PH PT
WC WJ WH WT
FC FJ FH FT
From the table, we can see that there are
12 different choices of food and drink.

11. You can get the total number of possible
outcomes by using a tree diagram or a table;
however, it is time consuming. You can use
Fundamental counting Principle to easily find
the total outcomes by multiplying the
outcomes of each individual event. Thus, If a
choice consists of many steps, the first of
which can be done in p ways, the second can
be done in q ways, the third can be done in r
ways, and so on, then the whole choice can be
made in p x q x r … ways.

12. Example 1: Tree Diagrams.
A new polo shirt is released in 4 different
colors and 5 different sizes. How many
different color and size combinations are
available to the public?
Colors – (Red, Blue, Green, Yellow)
Sizes – (S, M, L, XL, XXL)

13. Counting Outcomes
Example 1: Tree Diagrams.
Answer.
Red Blue Green Yellow
S M L XL XXL S M L XL XXL
S M L XL XXL S M L XL XXL
There are 20 different combinations.

14. Example 1: The Fundamental Counting
Principle.
A new polo shirt is released in 4 different
colors and 5 different sizes. How many
different color and size combinations are
available to the public?
Colors – (Red, Blue, Green, Yellow)
Sizes – (S, M, L, XL, XXL)

15. Counting Outcomes
Example 1: The Fundamental Counting
Principle.
Answer.
Number of Number of Number of
Possible Colors Possible Sizes Possible Comb.
4 x 5 = 20

16.  Tree Diagrams and The Fundamental
Counting Principle are two different
algorithms for finding sample space of
a probability problem.
 However, tree diagrams work better
for some problems and the
fundamental counting principle works
better for other problems.

17. Example 2:
If ice cream sundaes come in 5 flavors
with 4 possible toppings, how many
different sundaes can be made with
one flavor of ice cream and one
topping?
Solution:
5 x 4 = 20 possible sundaes.

18. Example 3:
A school canteen has a special lunch which
consists of rice, soup, viand, drinks, and dessert
for P90.00. They offer the following choices:
Rice: plain, fried
Viand: adobo, pakbet, sinigang, fried fish
Dessert: banana, cookie
Drinks: coffee, fruit juice, hot chocolate
How many special lunch are there?
Solution:
2 x 4 x 2 x 3 = 48 possible special lunch

19. Guided Practice: Answer each question.
(1) How many outfits are possible from a pair
of jean or khaki shorts and a choice of
yellow, white, or blue shirt?
(2) Scott has 5 shirts, 3 pairs of pants, and 4
pairs of socks. How many different outfits
can Scott choose with a shirt, pair of
pants, and pair of socks?

20. Guided Practice: Determine the probability
for each problem.
(1) Jean Shorts Khaki Shorts
Yellow White Blue Yellow White Blue
JSYS1 JSWS2 JSBS3 KSYS4 KSWS5 KSBS6
(2) Number Number Number Number
Of Shirts Of Pants Of Socks Of Outfits
5 x 3 x 4 = 60

21. Activity: Analyze each problem then solve.
(1) Suppose the graduation requirement for other
universities was that a student will take one course in
Mathematics and one course in Computer Science. If there
were 5 Math courses and 4 Computer Science courses
available, in how many ways could students meet this
requirement?
(2) Three friends want to spend the evening watching videos
overnight. One wants to watch a Korean movie; another
wants an action movie and the third wants a horror movie. If
there are 40 Korean movies, 100 action movies, and 35
horror movies available, in how many ways different sets of
three movies could these three select?

22. (3) Chloe has 9 shirts, 8 pairs of shoes, 7 jewelry
sets, and skirts. In how many different ways can
she dress up?
(4) A dormitory has 5 entrances and 4 exits. In how
many ways can students enter and leave the place
by a different door?
(5) Burger Queen offers 4 types of burgers, 5
types of beverages, and 3 types of desserts. If a
meal consists of 1 burger, 1 beverage, and 1
dessert, how many possible meals can be chosen?

23. Assignment:
Answer the following problems. Show your
solution.
1. A plate number is made up of three letters from
the English alphabet followed by a three-digit
number. How many plate numbers are possible to
form if:
a. the letters and digits can be repeated in
the same plate number?
b. the letters and digits cannot be
repeated in the same plate number?
2. How many 4-digit codes can be formed from the
digits 1,3,5,7, and 9 if repetition of digits is not
allowed?