Factorial Notation

Topics

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 4

1. Question
On the following events, write $\mathsf{P}$ if it is a Permutation or $\mathsf{C}$ if it is a Combination.
- $(i)$ Forming a doubles team for tennis: (C, c)
  
  $(ii)$ Creating a password for a website: (P, p)
  
  $(iii)$ Selecting the $1$ st, $2$ nd and $3$ rd rankings in a car race: (P, p)
  
  $(iv)$ Being a member of a jury: (C, c)
Correct

Keep Going!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Permutation

An arrangement where order is important.

Combination

A grouping where order is not important.

In each item, check whether the order is important or not

$(i)$ Forming a doubles team for tennis:

The order of tennis players in forming a doubles team for tennis is not important.

Hence, this is a Combination

$(ii)$ Creating a password for a website:

The order of characters in creating a password for a website is important.

Hence, this is a Permutation

$(iii)$ Selecting the $1$ st, $2$ nd and $3$ rd rankings in a car race:

The order or rankings in a car race is important.

Hence, this is a Permutation

$(iv)$ Being a member of a jury:

The order of being selected as a member in a jury is not important.

Hence, this is a Combination

$(i)$ $\mathsf{C}$

$(ii)$ $\mathsf{P}$

$(iii)$ $\mathsf{P}$

$(iv)$ $\mathsf{C}$
Question 2 of 4

2. Question
Evaluate

$5!$
- (120)
Hint

Help Video
Correct

Well Done!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Factorial Formula

$n! = n*(n-1)*(n-2)*…*3*2*1$

Substitute the given $n=5$ to the formula

$n!$ $=$ $n*(n-1)*(n-2)*…*3*2*1$ Factorial Formula

$5!$ $=$ $5*4*3*2*1$ Substitute known values

$=$ $120$

$120$

Question 3 of 4

Evaluate

$(12!)/(10!)$

(132)

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Factorial Formula

$n! = n*(n-1)*(n-2)*…*3*2*1$

Apply the formula to the fraction

$n_1$	$=$	$12$
$n_2$	$=$	$10$

$(n_1!)/(n_2!)$	$=$	$(n_1(n_1-1)(n_1-2)…321)/(n_2(n_2-1)(n_2-2)…321)$	Factorial Formula

$(12!)/(10!)$	$=$	$\frac{12\cdot11\cdot\color{#CC0000}{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}}{\color{#CC0000}{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}}$	Substitute known values

	$=$	$12*11$	Cancel like terms
	$=$	$132$

$132$

Question 4 of 4

Evaluate

$(9!)/(0!)$

(362880)

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Factorial Formula

$n! = n*(n-1)*(n-2)*…*3*2*1$

Zero Factorial

$0! = 1$

Apply the formula to the fraction

$n_1$	$=$	$9$
$n_2$	$=$	$0$

$(n_1!)/(n_2!)$	$=$	$(n_1(n_1-1)(n_1-2)…321)/(n_2(n_2-1)(n_2-2)…321)$	Factorial Formula

$(9!)/(0!)$	$=$	$\frac{9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{1}$	$0! =1$

	$=$	$362 880$

$362 880$

Factorial Notation

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Keep Going!

Permutation

Combination

2. Question

Hint

Well Done!

Factorial Formula

3. Question

Hint

Nice Job!

Factorial Formula

4. Question

Hint

Excellent!

Factorial Formula

Zero Factorial

Quizzes

$n!$	$=$	$n(n-1)(n-2)…321$	Factorial Formula
$5!$	$=$	$54321$	Substitute known values
	$=$	$120$