I.
Content Standard
Demonstrates understanding of key concepts of combinatorics and
probability.
II.
Learning competencies
a) Count the number of occurrence of an event.
b) Determine the permutation of objects with or without repetition;
c) Apply permutation in real life situation.
III.
IV.
V.
Content
Permutation
Learning resources
Procedure
A. elicit
Do you arrange objects at your home or on school?
B. Engage
Have you try to forgot the PIN code of your phone?
How do you recover your PIN?
C. Explore
Directions:
1. Divide the class into 4 groups.
2. Work with your groupmates and select one person to present
your output.
3. Do this for 5 min.
Group 1. How many ways you can arrange 1, 2, 3, & 4 without
repetition. List down the possible
outcomes
Group 2. How many ways you can arrange the letters STAR without
repetitions. List down the
possible outcomes.
Group 3. How many ways you can form ABC when repetition is
allowed? List down the possible
outcomes.
Group 4. How many ways you can arrange 1, 2, 3 when repetition is
allowed? List down the
possible outcomes.
Presentation…
D. Explain
Factorial
Definition:
For any natural number
𝑛! = 𝑛(𝑛 − 1)(𝑛 − 2)(𝑛 − 3) ⋅ … ⋅ 2 ⋅ 1.
The expression is read as “n Factorial.”
Examples:
1. 4!
2. 9!
Solution:
1. 4! = 4 ⋅ 3 ⋅ 2 ⋅ 1 = 24
2. 9! = 9 ⋅ 8 ⋅ 7 ⋅ 6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1 =
362,880
Practice:
1. 6!
2. 8!
3. 12!
Solution:
1. 6! = 720
2. 8! = 40320
3. 12! = 479001600
Definition:
𝟎! = 𝟏
Definition:
The permutation of objects taken 𝑛 at a time is denoted by
𝑛 𝑃𝑛 , where
𝑛𝑃𝑛 = 𝑛 ⋅ (𝑛 − 1) ⋅ (𝑛 − 2) ⋅ (𝑛 − 3) ⋅ … ⋅ 3 ⋅ 2 ⋅ 1
Example
1.
5 𝑃5
Solution:
1.
5 𝑃5 = 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1 = 120
2.
6 𝑃6
Practice:
1.
8 𝑃8
2.
7 𝑃7
2.
6 𝑃6 = 6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1 = 720
Solution:
1.
8 𝑃8 = 40320
2.
7 𝑃7 = 5040
E. Elaborate
Activity: Make a bookmark
What have you learned about permutation so far?
F. Evaluate
1. Using 1, 2, 3, 4, 5, how many 3-digit numbers greater than 200 can be
formed?
i.
ii.
Repetition not allowed.
Repetition allowed.
Evaluate the following:
1. 8!/4!
2.
4 𝑃4
2!
G. Extend
Activity: ATM
Direction.
You must choose a new 4-digit ATM pin number from the numbers 5, 0, 3, 8.
List all the possible pin numbers in the space below.
How many pin numbers in total are possible?
How many of these pin numbers begin with 3?
How many of these pin numbers are greater than 4000?
Can you come up with an easier way of arriving at your answer for the
above question?
How many of these pin numbers are less than 1000?
How many of the pin numbers are odd numbers?
What are the chances that your pin number is odd?