Fundamental Counting Principle 2

Topics

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 6

1. Question
A car dealer sells cars in $5$ colors (white, red, brown, yellow and green), $3$ interior trims (grey, black and red), $2$ transmission types (auto and manual), and $3$ model types (base, sport, luxury). What are the total number of choices you have as a customer?
- (90)
Hint

Help Video
Correct

Well Done!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Fundamental Counting Principle

number of ways $=$ $m$ $times$ $n$

First, list down all the categories and count the options for each

Color:

$=$ $5$

Interior:

$=$ $3$

Transmission:

Auto, Manual

$=$ $2$

Model:

Base, Sports, Luxury

$=$ $3$

Use the Fundamental Counting Principle and for each category multiply the number of options.

number of ways $=$ $m$ $times$ $n$ Fundamental Counting Principle

$=$ $5$ $times$ $3$ $times$ $2$ $times$ $3$

$=$ $90$

The total choices you have as a customer is $90$ .

$90$

Question 2 of 6

A car dealer sells cars in

$5$ colors (white, red, brown, yellow and green),

$3$ interior trims (grey, black and red),

$2$ transmission types (auto and manual), and

$3$ model types (base, sport, luxury). However, he can only have up to

$9$ cars on his lot. What is the probability that the car you want is in this lot?

Write fractions as “a/b”

(1/10)

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Probability

$\frac{\color{#e65021}{\mathsf{favourable\:outcome}}}{\color{#007DDC}{\mathsf{total\:outcome}}}$

Fundamental Counting
Principle

number of ways

$=$ $m$

$times$ $n$

First, list down all the categories and count the options for each

Color:

$=$ $5$

Interior:

$=$ $3$

Transmission:

Auto, Manual

$=$ $2$

Model:

Base, Sports, Luxury

$=$ $3$

Use the Fundamental Counting Principle and for each category multiply the number of options.

number of ways	$=$	$m$ $times$ $n$	Fundamental Counting Principle
	$=$	$5$ $times$ $3$ $times$ $2$ $times$ $3$
	$=$	$90$

Hence, the total outcome is $90$ .

Remember that the parking lot can have up to

$9$ cars. This means that the favourable outcome is $9$ .

Compute for the probability.

Probability	$=$	$\frac{\color{#e65021}{\mathsf{favourable\:outcome}}}{\color{#007DDC}{\mathsf{total\:outcome}}}$

	$=$	$\frac{\color{#e65021}{\mathsf{9}}}{\color{#007DDC}{\mathsf{90}}}$

	$=$	$1/10$

The probability that the car you want is in the parking lot is

$1/10$

Question 3 of 6

3. Question
A license plate has $3$ numbers and $3$ letters on it. How many possible combination of numbers and letters can be used?
- (17576000)
Hint

Help Video
Correct

Keep Going!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Fundamental Counting Principle

number of ways $=$ $m$ $times$ $n$

First, list down all the categories and count the options for each

Numbers:

$0-9$

$=$ $10$

Letters:

$A-Z$

$=$ $26$

Use the Fundamental Counting Principle and for each category multiply the number of options.

Remember that the license plate has three numbers and three letters.

number of ways $=$ $m$ $times$ $n$ Fundamental Counting Principle

$=$ $10$ $times$ $10$ $times$ $10$ $times$ $26$ $times$ $26$ $times$ $26$

$=$ $10^3times26^3$

$=$ $17 576 000$

The total combinations that can be used as a license plate is $17 576 000$ .

$17 576 000$
Question 4 of 6

4. Question
A license plate has $4$ letters and $2$ numbers on it. How many possible combination of numbers and letters can be used?
- (45697600)
Hint

Help Video
Correct

Excellent!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Fundamental Counting Principle

number of ways $=$ $m$ $times$ $n$

First, list down all the categories and count the options for each

Letters:

$A-Z$

$=$ $26$

Numbers:

$0-9$

$=$ $10$

Use the Fundamental Counting Principle and for each category multiply the number of options.

Remember that the license plate has four letters and two numbers.

number of ways $=$ $m$ $times$ $n$ Fundamental Counting Principle

$=$ $26$ $times$ $26$ $times$ $26$ $times$ $26$ $times$ $10$ $times$ $10$

$=$ $26^4times10^2$

$=$ $45 697 600$

The total combinations that can be used as a license plate is $45 697 600$ .

$45 697 600$
Question 5 of 6

5. Question
There are $5$ different marbles inside a jar. How many ways can you draw a marble $3$ times if you put back the drawn marble in the jar before drawing another one?
- (125)
Hint

Help Video
Correct

Well Done!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Fundamental Counting Principle

number of ways $=$ $m$ $times$ $n$

First, list down all the categories and count the options for each

First Draw:

$=$ $5$

Second Draw:

$=$ $5$

Third Draw:

$=$ $5$

Use the Fundamental Counting Principle and for each category multiply the number of options.

number of ways $=$ $m$ $times$ $n$ Fundamental Counting Principle

$=$ $5$ $times$ $5$ $times$ $5$

$=$ $125$

There are $125$ ways for you to draw the marbles.

$125$
Question 6 of 6

6. Question
There are $5$ different marbles inside a jar. How many ways can you draw a marble $3$ times if you don’t put back the drawn marbles in the jar?
- (60)
Hint

Help Video
Correct

Correct!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Fundamental Counting Principle

number of ways $=$ $m$ $times$ $n$

First, list down all the categories and count the options for each

First Draw:

$=$ $5$

Second Draw:

$=$ $4$

Third Draw:

$=$ $3$

Use the Fundamental Counting Principle and for each category multiply the number of options.

number of ways $=$ $m$ $times$ $n$ Fundamental Counting Principle

$=$ $5$ $times$ $4$ $times$ $3$

$=$ $60$

There are $60$ ways for you to draw the marbles.

$60$

Fundamental Counting Principle 2

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Well Done!

Fundamental Counting Principle

2. Question

Hint

Great Work!

Probability

Fundamental Counting
Principle

3. Question

Hint

Keep Going!

Fundamental Counting Principle

4. Question

Hint

Excellent!

Fundamental Counting Principle

5. Question

Hint

Well Done!

Fundamental Counting Principle

6. Question

Hint

Correct!

Fundamental Counting Principle

Quizzes