Fundamental Counting Principle 2

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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)
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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)

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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)
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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)
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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)
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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)
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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

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