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)

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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 phone number has eight digits.

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

The total combinations that can be used as a phone number is $100 000 000$ $100 000 000$ .

100 000 000

$100 000 000$

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)

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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 phone number has eight digits and the value decreases every digit.

number of ways	$=$ $=$	$m$ $m$ $\times$ $times$ $n$ $n$	Fundamental Counting Principle
	$=$ $=$	$10$ $10$ $\times$ $times$ $9$ $9$ $\times$ $times$ $8$ $8$ $\times$ $times$ $7$ $7$ $\times$ $times$ $6$ $6$
		$\times$ $times$ $5$ $5$ $\times$ $times$ $4$ $4$ $\times$ $times$ $3$ $3$
	$=$ $=$	$1 814 400$ $1 814 400$

The total combinations that can be used as a phone number is $1 814 400$ $1 814 400$ .

1 814 400

$1 814 400$

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

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

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

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

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

$10 000$ $10 000$
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

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

$10+26$

=

$=$ $36$ $36$

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

Remember that the password has five characters.

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

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

60 466 176

$60 466 176$

Question 6 of 6

6. Question
You are asked to create a $5$ $5$ -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 $=$ $=$ $m$ $m$ $\times$ $times$ $n$ $n$

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:

$10 + 26$ $10+26$

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

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 $=$ $=$ $m$ $m$ $\times$ $times$ $n$ $n$ Fundamental Counting Principle

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

$=$ $=$ $45 239 040$ $45 239 040$

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

$45 239 040$ $45 239 040$

Fundamental Counting Principle 3

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