Fundamental Counting Principle 2

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Question 1 of 6

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

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

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

Color:

$=$ $=$ $5$ $5$

Interior:

$=$ $=$ $3$ $3$

Transmission:

Auto, Manual

$=$ $=$ $2$ $2$

Model:

Base, Sports, Luxury

$=$ $=$ $3$ $3$

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

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

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

$=$ $=$ $90$ $90$

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

$90$ $90$

Question 2 of 6

A car dealer sells cars in

5

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

3

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

2

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

3

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

9

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

Write fractions as “a/b”

(1/10)

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Probability

\frac{f a v o u r a b l e o u t c o m e}{t o t a l o u t c o m e}

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

Fundamental Counting
Principle

number of ways

=

$=$ $m$ $m$

\times

$times$ $n$ $n$

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

Color:

=

$=$ $5$ $5$

Interior:

=

$=$ $3$ $3$

Transmission:

Auto, Manual

=

$=$ $2$ $2$

Model:

Base, Sports, Luxury

=

$=$ $3$ $3$

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

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

Hence, the total outcome is $90$ $90$ .

Remember that the parking lot can have up to

9

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

Compute for the probability.

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

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

	$=$ $=$	$\frac{1}{10}$ $1/10$

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

\frac{1}{10}

$1/10$

\frac{1}{10}

$1/10$

Question 3 of 6

A license plate has

3

$3$ numbers and

3

$3$ letters on it. How many possible combination of numbers and letters can be used?

(17576000)

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Fundamental Counting Principle

number of ways

=

$=$ $m$ $m$

\times

$times$ $n$ $n$

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

Numbers:

0 - 9

$0-9$

=

$=$ $10$ $10$

Letters:

A - Z

$A-Z$

=

$=$ $26$ $26$

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	$=$ $=$	$m$ $m$ $\times$ $times$ $n$ $n$	Fundamental Counting Principle
	$=$ $=$	$10$ $10$ $\times$ $times$ $10$ $10$ $\times$ $times$ $10$ $10$ $\times$ $times$ $26$ $26$ $\times$ $times$ $26$ $26$ $\times$ $times$ $26$ $26$
	$=$ $=$	$10^{3} \times 26^{3}$ $10^3times26^3$
	$=$ $=$	$17 576 000$ $17 576 000$

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

17 576 000

$17 576 000$

Question 4 of 6

A license plate has

4

$4$ letters and

2

$2$ numbers on it. How many possible combination of numbers and letters can be used?

(45697600)

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Fundamental Counting Principle

number of ways

=

$=$ $m$ $m$

\times

$times$ $n$ $n$

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

Letters:

A - Z

$A-Z$

=

$=$ $26$ $26$

Numbers:

0 - 9

$0-9$

=

$=$ $10$ $10$

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	$=$ $=$	$m$ $m$ $\times$ $times$ $n$ $n$	Fundamental Counting Principle
	$=$ $=$	$26$ $26$ $\times$ $times$ $26$ $26$ $\times$ $times$ $26$ $26$ $\times$ $times$ $26$ $26$ $\times$ $times$ $10$ $10$ $\times$ $times$ $10$ $10$
	$=$ $=$	$26^{4} \times 10^{2}$ $26^4times10^2$
	$=$ $=$	$45 697 600$ $45 697 600$

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

45 697 600

$45 697 600$

Question 5 of 6

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

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

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

First Draw:

$=$ $=$ $5$ $5$

Second Draw:

$=$ $=$ $5$ $5$

Third Draw:

$=$ $=$ $5$ $5$

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

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

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

$=$ $=$ $125$ $125$

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

$125$ $125$
Question 6 of 6

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

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

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

First Draw:

$=$ $=$ $5$ $5$

Second Draw:

$=$ $=$ $4$ $4$

Third Draw:

$=$ $=$ $3$ $3$

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

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

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

$=$ $=$ $60$ $60$

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

$60$ $60$

Fundamental Counting Principle 2

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