Topics
>
Statistics and Probability>
Combinations and Permutations>
Fundamental Counting Principle>
Fundamental Counting Principle 1Fundamental Counting Principle 1
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
There are four paths going from Town `1` to Town `2`, and two paths going from Town `2` to Town `3`.
How many possible paths can you take to go from Town `1` to Town `3`?
- (8)
Hint
Help VideoCorrect
Great Work!
Incorrect
Fundamental Counting Principle
number of ways `=``m``times``n`First, set up a diagram for the problem for easier visualizationFirst, list down all the categories and count the options for eachPaths from Town 1 to Town 2:
`=``4`Paths from Town 2 to Town 3:
`=``2`Use the Fundamental Counting Principle and for each category multiply the number of options.number of ways `=` `m``times``n` Fundamental Counting Principle `=` `4``times``2` `=` `8` The total paths that you can take is `8`.`8` -
Question 2 of 6
2. Question
A restaurant offers three entrees (Soup, Salad, Cheese Soufle), three main courses (Roast Beef, Chicken, Salmon) and four desserts (Chocolate Cake, Strawberry Trifle, Ice Cream, Chocolate Sundae). How many three-course meals can you have?
- (36)
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 eachEntree:
`=``3`Main Course:
`=``3`Dessert:
`=``4`Use the Fundamental Counting Principle and for each category multiply the number of options.number of ways `=` `m``times``n` Fundamental Counting Principle `=` `3``times``3``times``4` `=` `36` You can have `36` different three-meal courses.`36` -
Question 3 of 6
3. Question
A restaurant offers three entrees (Soup, Salad, Cheese Soufle), three main courses (Roast Beef, Chicken, Salmon) and four desserts (Chocolate Cake, Strawberry Trifle, Ice Cream, Chocolate Sundae). What is the possibility that someone chose a meal that you wanted given that they know you don’t want the soup?
Write fractions as “a/b”- (1/24)
Hint
Help VideoCorrect
Keep Going!
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 eachEntree:
`=``2`Main Course:
`=``3`Dessert:
`=``4`Use the Fundamental Counting Principle and for each category multiply the number of options.number of ways `=` `m``times``n` Fundamental Counting Principle `=` `2``times``3``times``4` `=` `24` You can have `24` different three-meal courses which is the total outcome.You only want to have a specific three-course meal. This means that the favourable outcome
is `1`.Compute for the probability.Probability `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcome}}}{\color{#007DDC}{\mathsf{total\:outcome}}}$$ `=` $$\frac{\color{#e65021}{\mathsf{1}}}{\color{#007DDC}{\mathsf{24}}}$$ The probability that the meal picked for you is the one you wanted is `1/24``1/24` -
Question 4 of 6
4. Question
A diner offers a four-course lunch with an entree (Burger, Sandwich, Taco, Pizza), a side meal (Soup, Salad, French Fries),
a beverage (Lemonade, Cola, Coffee) and a dessert (Cake, Ice Cream). How many possible meals can you have?
- (72)
Hint
Help VideoCorrect
Fantastic!
Incorrect
Fundamental Counting Principle
number of ways `=``m``times``n`First, list down all the categories and count the options for eachEntree:
`=``4`Side:
`=``3`Beverage:
`=``3`Dessert:
`=``2`Use the Fundamental Counting Principle and for each category multiply the number of options.number of ways `=` `m``times``n` Fundamental Counting Principle `=` `4``times``3``times``3``times``2` `=` `72` You can have `72` different four-meal courses.`72` -
Question 5 of 6
5. Question
A diner offers a four-course lunch with an entree (Burger, Sandwich, Taco, Pizza), a side meal (Soup, Salad, French Fries),
a beverage (Lemonade, Cola, Coffee) and a dessert (Cake, Ice Cream). How many possible meals can you have if you won’t be having any beverages?
- (24)
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 eachEntree:
`=``4`Side:
`=``3`Dessert:
`=``2`Use the Fundamental Counting Principle and for each category multiply the number of options.number of ways `=` `m``times``n` Fundamental Counting Principle `=` `4``times``3``times``2` `=` `24` You can have `24` different set of meals.`24` -
Question 6 of 6
6. Question
A diner offers a four-course lunch with an entree (Burger, Sandwich, Taco, Pizza), a side meal (Soup, Salad, French Fries),
a beverage (Lemonade, Cola, Coffee) and a dessert (Cake, Ice Cream). How many possible meals can you have if the diner ran out of pizza and ice cream?
- (27)
Hint
Help VideoCorrect
Nice Job!
Incorrect
Fundamental Counting Principle
number of ways `=``m``times``n`First, list down all the categories and count the options for eachEntree:
`=``3`Side:
`=``3`Beverage:
`=``3`Dessert:
`=``1`Use the Fundamental Counting Principle and for each category multiply the number of options.number of ways `=` `m``times``n` Fundamental Counting Principle `=` `3``times``3``times``3``times``1` `=` `27` You can have `27` different set of meals.`27`
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