Fundamental Counting Principle 1

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Question 1 of 6

1. Question
There are four paths going from Town $1$ $1$ to Town $2$ $2$ , and two paths going from Town $2$ $2$ to Town $3$ $3$ .
How many possible paths can you take to go from Town $1$ $1$ to Town $3$ $3$ ?
- (8)
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Fundamental Counting Principle

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

First, set up a diagram for the problem for easier visualization

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

Paths from Town 1 to Town 2:

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

Paths from Town 2 to Town 3:

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

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

$=$ $=$ $4$ $4$ $\times$ $times$ $2$ $2$

$=$ $=$ $8$ $8$

The total paths that you can take is $8$ $8$ .

$8$ $8$
Question 2 of 6

2. Question
A restaurant offers three entrees (Soup, Salad, Cheese Soufle), three main courses (Roast Beef, Chicken, Salmon) and four desserts (Chocolate Cake, Strawberry Trifle, Ice Cream, Chocolate Sundae). How many three-course meals can you have?
- (36)
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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

Entree:

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

Main Course:

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

Dessert:

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

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

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

$=$ $=$ $36$ $36$

You can have $36$ $36$ different three-meal courses.

$36$ $36$

Question 3 of 6

A restaurant offers three entrees (Soup, Salad, Cheese Soufle), three main courses (Roast Beef, Chicken, Salmon) and four desserts (Chocolate Cake, Strawberry Trifle, Ice Cream, Chocolate Sundae). What is the possibility that someone chose a meal that you wanted given that they know you don’t want the soup?

Write fractions as “a/b”

(1/24)

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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

Entree:

$=$ $2$

Main Course:

$=$ $3$

Dessert:

$=$ $4$

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

number of ways	$=$	$m$ $times$ $n$	Fundamental Counting Principle
	$=$	$2$ $times$ $3$ $times$ $4$
	$=$	$24$

You can have $24$ different three-meal courses which is the total outcome.

You only want to have a specific three-course meal. This means that the favourable outcome
is $1$ .

Compute for the probability.

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

	$=$	$\frac{\color{#e65021}{\mathsf{1}}}{\color{#007DDC}{\mathsf{24}}}$

The probability that the meal picked for you is the one you wanted is

$1/24$

Question 4 of 6

4. Question
A diner offers a four-course lunch with an entree (Burger, Sandwich, Taco, Pizza), a side meal (Soup, Salad, French Fries),
a beverage (Lemonade, Cola, Coffee) and a dessert (Cake, Ice Cream). How many possible meals can you have?
- (72)
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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

Entree:

$=$ $4$

Side:

$=$ $3$

Beverage:

$=$ $3$

Dessert:

$=$ $2$

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

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

$=$ $4$ $times$ $3$ $times$ $3$ $times$ $2$

$=$ $72$

You can have $72$ different four-meal courses.

$72$
Question 5 of 6

5. Question
A diner offers a four-course lunch with an entree (Burger, Sandwich, Taco, Pizza), a side meal (Soup, Salad, French Fries),
a beverage (Lemonade, Cola, Coffee) and a dessert (Cake, Ice Cream). How many possible meals can you have if you won’t be having any beverages?
- (24)
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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

Entree:

$=$ $4$

Side:

$=$ $3$

Dessert:

$=$ $2$

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

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

$=$ $4$ $times$ $3$ $times$ $2$

$=$ $24$

You can have $24$ different set of meals.

$24$
Question 6 of 6

6. Question
A diner offers a four-course lunch with an entree (Burger, Sandwich, Taco, Pizza), a side meal (Soup, Salad, French Fries),
a beverage (Lemonade, Cola, Coffee) and a dessert (Cake, Ice Cream). How many possible meals can you have if the diner ran out of pizza and ice cream?
- (27)
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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

Entree:

$=$ $3$

Side:

$=$ $3$

Beverage:

$=$ $3$

Dessert:

$=$ $1$

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

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

$=$ $3$ $times$ $3$ $times$ $3$ $times$ $1$

$=$ $27$

You can have $27$ different set of meals.

$27$

Fundamental Counting Principle 1

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Quiz summary

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1. Question

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Fundamental Counting Principle

2. Question

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Fundamental Counting Principle

3. Question

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Probability

Fundamental Counting
Principle

4. Question

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Fundamental Counting Principle

5. Question

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Fundamental Counting Principle

6. Question

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Fundamental Counting Principle

Quizzes

number of ways	$=$ $=$	$m$ $m$ $\times$ $times$ $n$ $n$	Fundamental Counting Principle
	$=$ $=$	$4$ $4$ $\times$ $times$ $2$ $2$
	$=$ $=$	$8$ $8$