1. Home
  2. Algebra and trigonometry
  3. Sequences, probability, and
  4. Counting principles

13.5 Counting principles

<< Chapter < Page
  Algebra and trigonometry     Page 1 / 12
Chapter >> Page >
In this section, you will:
  • Solve counting problems using the Addition Principle.
  • Solve counting problems using the Multiplication Principle.
  • Solve counting problems using permutations involving n distinct objects.
  • Solve counting problems using combinations.
  • Find the number of subsets of a given set.
  • Solve counting problems using permutations involving n non-distinct objects.

A new company sells customizable cases for tablets and smartphones. Each case comes in a variety of colors and can be personalized for an additional fee with images or a monogram. A customer can choose not to personalize or could choose to have one, two, or three images or a monogram. The customer can choose the order of the images and the letters in the monogram. The company is working with an agency to develop a marketing campaign with a focus on the huge number of options they offer. Counting the possibilities is challenging!

We encounter a wide variety of counting problems every day. There is a branch of mathematics devoted to the study of counting problems such as this one. Other applications of counting include secure passwords, horse racing outcomes, and college scheduling choices. We will examine this type of mathematics in this section.

Using the addition principle

The company that sells customizable cases offers cases for tablets and smartphones. There are 3 supported tablet models and 5 supported smartphone models. The Addition Principle tells us that we can add the number of tablet options to the number of smartphone options to find the total number of options. By the Addition Principle, there are 8 total options, as we can see in [link] .

The addition of 3 iPods and 4 iPhones.

The addition principle

According to the Addition Principle    , if one event can occur in m ways and a second event with no common outcomes can occur in n ways, then the first or second event can occur in m + n ways.

Using the addition principle

There are 2 vegetarian entrée options and 5 meat entrée options on a dinner menu. What is the total number of entrée options?

We can add the number of vegetarian options to the number of meat options to find the total number of entrée options.

The addition of the type of options for an entree.

There are 7 total options.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

A student is shopping for a new computer. He is deciding among 3 desktop computers and 4 laptop computers. What is the total number of computer options?

7

Got questions? Get instant answers now!

Using the multiplication principle

The Multiplication Principle applies when we are making more than one selection. Suppose we are choosing an appetizer, an entrée, and a dessert. If there are 2 appetizer options, 3 entrée options, and 2 dessert options on a fixed-price dinner menu, there are a total of 12 possible choices of one each as shown in the tree diagram in [link] .

A tree diagram of the different menu combinations.

The possible choices are:

  1. soup, chicken, cake
  2. soup, chicken, pudding
  3. soup, fish, cake
  4. soup, fish, pudding
  5. soup, steak, cake
  6. soup, steak, pudding
  7. salad, chicken, cake
  8. salad, chicken, pudding
  9. salad, fish, cake
  10. salad, fish, pudding
  11. salad, steak, cake
  12. salad, steak, pudding We can also find the total number of possible dinners by multiplying.

We could also conclude that there are 12 possible dinner choices simply by applying the Multiplication Principle.

Questions & Answers

it is the relatively stable flow of income
Chidubem Reply
what is circular flow of income
Divine Reply
branches of macroeconomics
SHEDRACK Reply
what is Flexible exchang rate?
poudel Reply
is gdp a reliable measurement of wealth
Atega Reply
introduction to econometrics
Husseini Reply
Hi
mostafa
hi
LEMLEM
hello
Sammol
hi
Mahesh
bi
Ruqayat
hi
Ruqayat
Hi fellas
Nyawa
hey
Sammol
hi
God
hello
Jahara
Good morning
Jorge
hi
abubakar
hi
Nmesoma
hi
Mahesh
Hi
Tom
Why is unemployment rate never zero at full employment?
Priyanka Reply
bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
Rushawn Reply
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost 6% more than previous year? Provide with reasoning.
Geetha Reply
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Waeth
discus major problems of macroeconomics
Alii Reply
what is the problem of macroeconomics
Yoal
Economic growth Stable prices and low unemployment
Ephraim
explain inflationcause and itis degre
Miresa Reply
what is inflation
Getu
increase in general price levels
WEETO
Good day How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200. Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
Chisomo Reply
how to calculate actual output?
Chisomo
how to calculate the equilibrium income
Beshir
Criteria for determining money supply
Thapase Reply
who we can define macroeconomics in one line
Muhammad
Aggregate demand
Mohammed
C=k100 +9y and i=k50.calculate the equilibrium level of output
Mercy Reply
Hi
Isiaka
Hi
Geli
hy
Man
👋
Bahunda
hy how are you?
Man
ys
Amisha
how are you guys
Sekou
f9 guys
Amisha
how are you guys
Sekou
ys am also fine
Amisha
fine and you guys
Geli
from Nepal
Amisha
nawalparasi district from belatari
Amisha
nd u
Amisha
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ma management ho
Amisha
ahile becheclor ho
Amisha
hjr ktm bta ho ani k kaam grnu hunxa tw
Amisha
belatari
Amisha
1st year ho
Amisha
nd u
Amisha
ahh
Amisha
kaha biratnagar
Amisha
ys
Amisha
kina k vo
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9 no Mpc is greater than 1 Y=100+.9Y+50 Y-.9Y=150 0.1Y/0.1=150/0.1 Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output? discuss your answer using appropriate graph.
Galge Reply
if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
Kalombe
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>
Practice Key Terms 5

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask