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Fundamental Counting Principle 2Fundamental Counting Principle 2
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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)
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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)
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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)
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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)
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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)
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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)
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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`
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