Derive the formula to find the permutation of
n objects taken r at a time;
Find the permutation of n objects
taken r at a time; and
Value the concepts of permutations in
solving real-life situations.
Objective
s
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Permutation refers to the arrangement of objects in a specific order. It is a fundamental concept in combinatorics, a branch of mathematics concerned with counting and arrangement. Permutations are used to calculate the number of possible ways to arrange a set of items, where the order of arrangement matters.
Typology: Slides
2021/2022
1 / 28
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download Understanding Permutation and more Slides Mathematics in PDF only on Docsity!
Derive the formula to find the permutation of
n objects taken r at a time;
Find the permutation of n objects
taken r at a time; and
Value the concepts of permutations in
solving real-life situations.
Objective
s
Permutation
of n Objects
Taken r at a Time
Answer:
In how many ways can you place 9 different
books on a shelf if there is space enough for
only 5 books?
OI
Order is Important
Answer:
Suppose that in a certain association, there are
12 elected members of the Board of Directors.
In how many ways can a president, a vice
president, a secretary, and a treasurer be
selected from a board?
OI
Order is Important
Answer:
If Ron has 12 t-shirts, 6 pairs of pants and 3
pairs of shoes, how many possibilities can he
dress himself up for the day?
ONI
Order Not Important
Answer:
The school canteen serves tuna, chicken, and cheese
sandwiches. The drinks available are soft drinks or
iced tea. A student may also choose from the 5
flavors of ice cream. In how many ways can a value
meal be completed from the following choices,
consisting of a sandwich, a drink, and an ice cream?
ONI
Order Not Important
Methods in Determining Permutations
- Systematic Listing – is a method used to determine the
number of permutations made for each problems.
- Tree Diagram – is a simple way to illustrate the
possible outcomes of events.
- Fundamental Counting Principle (FCP)
Von invited his classmates Ranz, Niana and Seah
in his birthday party. He prepared a special table for
them with chairs arranged in a row.
- In how many ways can they be
seated in a row? List the
possibilities.
- Show another way of finding the answer in item 1.
R
N
S N
S
S
N
R N
R
N
R S
(Ranz, Niana, Seah)
(Ranz, Seah, Niana)
(Seah, Niana, Ranz)
(Seah, Ranz, Niana)
(Niana, Ranz, Seah)
(Niana, Seah, Ranz)
Tree Diagram
S R
Fundamental Counting Principle (FCP)
Solution:
3 2 1
N = 6
x x
The product of 6 x 5 x 4 x 3 x 2 x 1 may be
written as 6! (read as “6 factorial”).
5! = 5 x 4 x 3 x 2 x 1=
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1= 5 040
Examples:
0! = 1
The number of permutations of n objects taken n
at a time, is denoted by nPn is given by n!.
The factorial function (symbol: !) says to multiply all
whole numbers from our chosen number down to 1.
n! = n(n-1) (n-2) (n-3) …2(1) where n ≥
1
What if the permutation of n objects
taken r at a time?
The permutation of 6 families taken 3 at a time is
denoted by 6 P 3 , P(6, 3), P 6 , 3 , or.
Similarly, if there are n objects which will be arranged r
at a time, it will be denoted by nPr.