Fundamental Counting Principle 3

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Question 1 of 6

A phone number contains

8

$8$ digits. How many combinations of numbers are possible?

(100000000)

Question 2 of 6

A phone number contains

8

$8$ digits. How many combinations of numbers are possible if you can’t repeat a number?

(1814400)

Question 3 of 6

3. Question
You are asked to create a $4$ $4$ digit PIN. How many combinations of numbers are possible?
- (10000)
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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:

$0 - 9$ $0-9$

$=$ $=$ $10$ $10$

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

Remember that the PIN has four digits.

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

$=$ $=$ $10$ $10$ $\times$ $times$ $10$ $10$ $\times$ $times$ $10$ $10$ $\times$ $times$ $10$ $10$

$=$ $=$ $10^{4}$ $10^4$

$=$ $=$ $10000$ $10 000$

The total combinations that can be used as a PIN is $10000$ $10 000$ .

$10000$ $10 000$
Question 4 of 6

4. Question
You are asked to create a $4$ $4$ digit PIN. How many combinations of numbers are possible if you can’t repeat a number?
- (5040)
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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:

$0 - 9$ $0-9$

$=$ $=$ $10$ $10$

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

Remember that the PIN has four digits and the value decreases every digit.

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

$=$ $=$ $10$ $10$ $\times$ $times$ $9$ $9$ $\times$ $times$ $8$ $8$ $\times$ $times$ $7$ $7$

$=$ $=$ $5040$ $5040$

The total combinations that can be used as a PIN is $5040$ $5040$ .

$5040$ $5040$
Question 5 of 6

5. Question
You are asked to create a $5$ $5$ -character password. How many combinations of characters are possible?
- (60466176)
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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:

$A - Z$ $A-Z$

$= 26$ $=26$

Total Characters:

$10 + 26$ $10+26$

$=$ $36$

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

Remember that the password has five characters.

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

$=$ $36$ $times$ $36$ $times$ $36$ $times$ $36$ $times$ $36$

$=$ $36^5$

$=$ $60 466 176$

The total combinations that can be used as a password is $60 466 176$ .

$60 466 176$
Question 6 of 6

6. Question
You are asked to create a $5$ -character password. How many combinations of characters are possible if you can’t repeat a character?
- (45239040)
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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:

$A-Z$

$=26$

Total Characters:

$10+26$

$=$ $36$

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

Remember that the password has five characters and the value decreases every character.

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

$=$ $36$ $times$ $35$ $times$ $34$ $times$ $33$ $times$ $32$

$=$ $45 239 040$

The total combinations that can be used as a password is $45 239 040$ .

$45 239 040$

Fundamental Counting Principle 3

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Quiz summary

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1. Question

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Fantastic!

Fundamental Counting Principle

2. Question

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Fundamental Counting Principle

3. Question

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Well Done!

Fundamental Counting Principle

4. Question

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Great Work!

Fundamental Counting Principle

5. Question

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Nice Job!

Fundamental Counting Principle

6. Question

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Correct!

Fundamental Counting Principle

Quizzes

number of ways	$=$ $=$	$m$ $m$ $\times$ $times$ $n$ $n$	Fundamental Counting Principle
	$=$ $=$	$10$ $10$ $\times$ $times$ $10$ $10$ $\times$ $times$ $10$ $10$ $\times$ $times$ $10$ $10$ $\times$ $times$ $10$ $10$
		$\times$ $times$ $10$ $10$ $\times$ $times$ $10$ $10$ $\times$ $times$ $10$ $10$
	$=$ $=$	$10^{8}$ $10^8$
	$=$ $=$	$100000000$ $100 000 000$

number of ways	$=$	$m$ $times$ $n$	Fundamental Counting Principle
	$=$	$36$ $times$ $36$ $times$ $36$ $times$ $36$ $times$ $36$
	$=$	$36^5$
	$=$	$60 466 176$