30231

Question

{{name}} wants to make as many different {{type1}} as possible using the {{item1}}:


{{item2}}


{{phrase}}, how many different {{type2}} can she make?

Worked Solution

Number of possibilities:
1st {{item3}} : {{number1}}
2nd {{item3}} : {{number2}}
3rd {{item3}} : {{number3}}
4th {{item3}} : 1

∴\therefore Total possible {{type2}}
= {{number1}} ×\times {{number2}} ×\times {{number3}} ×\times 1
= {{{correctAnswer}}}

Variant 0

DifficultyLevel

540

Question

Dani wants to make as many different four-digit numbers as possible using the numbers:



In total, how many different numbers can she make?

Worked Solution

Number of possibilities:
1st digit : 4
2nd digit : 3
3rd digit : 2
4th digit : 1

∴\therefore Total possible numbers
= 4 ×\times 3 ×\times 2 ×\times 1
= 24

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
name
Dani
type1
four-digit numbers
item1
numbers
item2
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2020/08/Q52var1.svg 200 indent vpad
phrase
In total
type2
numbers
item3
digit
number1
4
number2
3
number3
2
correctAnswer
24

Answers

Is Correct?Answer
x

4

x

12

✓

24

x

7631

Variant 1

DifficultyLevel

540

Question

Cynthia wants to make as many different letter arrangements as possible using the four letters:



In total, how many different arrangements can she make?

Worked Solution

Number of possibilities:
1st letter : 4
2nd letter : 3
3rd letter : 2
4th letter : 1

∴\therefore Total possible arrangements
= 4 ×\times 3 ×\times 2 ×\times 1
= 24

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
name
Cynthia
type1
letter arrangements
item1
four letters
item2
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2020/08/Q52var2.svg 200 indent vpad
phrase
In total
type2
arrangements
item3
letter
number1
4
number2
3
number3
2
correctAnswer
24

Answers

Is Correct?Answer
x

4

x

12

✓

24

x

32

Variant 2

DifficultyLevel

540

Question

Jane wants to make as many different four digit numbers as possible using the numbers:



If the four digit number must start with 3, how many different number can she make?

Worked Solution

Number of possibilities:
1st numbers : 1
2nd numbers : 3
3rd numbers : 2
4th numbers : 1

∴\therefore Total possible number
= 1 ×\times 3 ×\times 2 ×\times 1
= 6

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
name
Jane
type1
four digit numbers
item1
numbers
item2
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2020/08/Q52var3.svg 200 indent vpad
phrase
If the four digit number must start with 3
item3
numbers
type2
number
number1
1
number2
3
number3
2
correctAnswer
6

Answers

Is Correct?Answer
x

3

✓

6

x

12

x

27

Variant 3

DifficultyLevel

540

Question

Gaby wants to make as many different letter arrangements as possible using the four letters:



If the letter arrangement must start with L, how many different arrangement can she make?

Worked Solution

Number of possibilities:
1st letter : 1
2nd letter : 3
3rd letter : 2
4th letter : 1

∴\therefore Total possible arrangement
= 1 ×\times 3 ×\times 2 ×\times 1
= 6

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
name
Gaby
type1
letter arrangements
item1
four letters
item2
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2020/08/Q52var4.svg 200 indent vpad
phrase
If the letter arrangement must start with L
type2
arrangement
item3
letter
number1
1
number2
3
number3
2
correctAnswer
6

Answers

Is Correct?Answer
✓

6

x

12

x

24

x

27

Variant 4

DifficultyLevel

540

Question

Miranda wants to make as many different side-by-side arrangements as possible using the four shapes:



In total, how many different arrangements can she make?

Worked Solution

Number of possibilities:
1st shape : 4
2nd shape : 3
3rd shape : 2
4th shape : 1

∴\therefore Total possible arrangements
= 4 ×\times 3 ×\times 2 ×\times 1
= 24

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
name
Miranda
type1
side-by-side arrangements
item1
four shapes
item2
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2020/08/Q51var5.svg 200 indent vpad
phrase
In total
type2
arrangements
item3
shape
number1
4
number2
3
number3
2
correctAnswer
24

Answers

Is Correct?Answer
x

4

x

12

✓

24

x

27