Years
>
Year 12>
Permutations and Combinations>
Fundamental Counting Principle>
Fundamental Counting Principle 2Fundamental Counting Principle 2
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 6 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
- 6
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- 5
- 6
- Answered
- Review
-
Question 1 of 6
1. Question
A car dealer sells cars in `5` colors (white, red, brown, yellow and green), `3` interior trims (grey, black and red), `2` transmission types (auto and manual), and `3` model types (base, sport, luxury). What are the total number of choices you have as a customer?
- (90)
Hint
Help VideoCorrect
Well Done!
Incorrect
Fundamental Counting Principle
number of ways `=``m``times``n`First, list down all the categories and count the options for eachColor:
`=``5`Interior:
`=``3`Transmission:Auto, Manual`=``2`Model:Base, Sports, Luxury`=``3`Use the Fundamental Counting Principle and for each category multiply the number of options.number of ways `=` `m``times``n` Fundamental Counting Principle `=` `5``times``3``times``2``times``3` `=` `90` The total choices you have as a customer is `90`.`90` -
Question 2 of 6
2. Question
A car dealer sells cars in `5` colors (white, red, brown, yellow and green), `3` interior trims (grey, black and red), `2` transmission types (auto and manual), and `3` model types (base, sport, luxury). However, he can only have up to `9` cars on his lot. What is the probability that the car you want is in this lot?Write fractions as “a/b”- (1/10)
Hint
Help VideoCorrect
Great Work!
Incorrect
Probability
$$\frac{\color{#e65021}{\mathsf{favourable\:outcome}}}{\color{#007DDC}{\mathsf{total\:outcome}}}$$Fundamental Counting
Principlenumber of ways `=``m``times``n`First, list down all the categories and count the options for eachColor:
`=``5`Interior:
`=``3`Transmission:Auto, Manual`=``2`Model:Base, Sports, Luxury`=``3`Use the Fundamental Counting Principle and for each category multiply the number of options.number of ways `=` `m``times``n` Fundamental Counting Principle `=` `5``times``3``times``2``times``3` `=` `90` Hence, the total outcome is `90`.Remember that the parking lot can have up to `9` cars. This means that the favourable outcome is `9`.Compute for the probability.Probability `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcome}}}{\color{#007DDC}{\mathsf{total\:outcome}}}$$ `=` $$\frac{\color{#e65021}{\mathsf{9}}}{\color{#007DDC}{\mathsf{90}}}$$ `=` `1/10` The probability that the car you want is in the parking lot is `1/10``1/10` -
Question 3 of 6
3. Question
A license plate has `3` numbers and `3` letters on it. How many possible combination of numbers and letters can be used?- (17576000)
Hint
Help VideoCorrect
Keep Going!
Incorrect
Fundamental Counting Principle
number of ways `=``m``times``n`First, list down all the categories and count the options for eachNumbers:`0-9``=``10`Letters:`A-Z``=``26`Use the Fundamental Counting Principle and for each category multiply the number of options.Remember that the license plate has three numbers and three letters.number of ways `=` `m``times``n` Fundamental Counting Principle `=` `10``times``10``times``10``times``26``times``26``times``26` `=` `10^3times26^3` `=` `17 576 000` The total combinations that can be used as a license plate is `17 576 000`.`17 576 000` -
Question 4 of 6
4. Question
A license plate has `4` letters and `2` numbers on it. How many possible combination of numbers and letters can be used?- (45697600)
Hint
Help VideoCorrect
Excellent!
Incorrect
Fundamental Counting Principle
number of ways `=``m``times``n`First, list down all the categories and count the options for eachLetters:`A-Z``=``26`Numbers:`0-9``=``10`Use the Fundamental Counting Principle and for each category multiply the number of options.Remember that the license plate has four letters and two numbers.number of ways `=` `m``times``n` Fundamental Counting Principle `=` `26``times``26``times``26``times``26``times``10``times``10` `=` `26^4times10^2` `=` `45 697 600` The total combinations that can be used as a license plate is `45 697 600`.`45 697 600` -
Question 5 of 6
5. Question
There are `5` different marbles inside a jar. How many ways can you draw a marble `3` times if you put back the drawn marble in the jar before drawing another one?
- (125)
Hint
Help VideoCorrect
Well Done!
Incorrect
Fundamental Counting Principle
number of ways `=``m``times``n`First, list down all the categories and count the options for eachFirst Draw:`=``5`Second Draw:`=``5`Third Draw:`=``5`Use the Fundamental Counting Principle and for each category multiply the number of options.number of ways `=` `m``times``n` Fundamental Counting Principle `=` `5``times``5``times``5` `=` `125` There are `125` ways for you to draw the marbles.`125` -
Question 6 of 6
6. Question
There are `5` different marbles inside a jar. How many ways can you draw a marble `3` times if you don’t put back the drawn marbles in the jar?
- (60)
Hint
Help VideoCorrect
Correct!
Incorrect
Fundamental Counting Principle
number of ways `=``m``times``n`First, list down all the categories and count the options for eachFirst Draw:
`=``5`Second Draw:
`=``4`Third Draw:
`=``3`Use the Fundamental Counting Principle and for each category multiply the number of options.number of ways `=` `m``times``n` Fundamental Counting Principle `=` `5``times``4``times``3` `=` `60` There are `60` ways for you to draw the marbles.`60`
Quizzes
- Factorial Notation
- Fundamental Counting Principle 1
- Fundamental Counting Principle 2
- Fundamental Counting Principle 3
- Combinations 1
- Combinations 2
- Combinations with Restrictions 1
- Combinations with Restrictions 2
- Combinations with Probability
- Basic Permutations 1
- Basic Permutations 2
- Basic Permutations 3
- Permutation Problems 1
- Permutation Problems 2
- Permutations with Repetitions 1
- Permutations with Repetitions 2
- Permutations with Restrictions 1
- Permutations with Restrictions 2
- Permutations with Restrictions 3
- Permutations with Restrictions 4