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Fundamental Counting Principle>
Fundamental Counting Principle 1Fundamental Counting Principle 1
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Question 1 of 6
1. Question
There are four paths going from Town 11 to Town 22, and two paths going from Town 22 to Town 33.
How many possible paths can you take to go from Town 11 to Town 33?- (8)
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Fundamental Counting Principle
number of ways ==mm××nnFirst, 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:==44Paths from Town 2 to Town 3:==22Use the Fundamental Counting Principle and for each category multiply the number of options.number of ways == mm××nn Fundamental Counting Principle == 44××22 == 88 The total paths that you can take is 88.88 -
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)
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Fundamental Counting Principle
number of ways ==mm××nnFirst, list down all the categories and count the options for eachEntree:==33Main Course:==33Dessert:==44Use the Fundamental Counting Principle and for each category multiply the number of options.number of ways == mm××nn Fundamental Counting Principle == 33××33××44 == 3636 You can have 3636 different three-meal courses.3636 -
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)
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Probability
favourableoutcometotaloutcomeFundamental Counting
Principlenumber of ways =m×nFirst, list down all the categories and count the options for eachEntree:=2Main Course:=3Dessert:=4Use the Fundamental Counting Principle and for each category multiply the number of options.number of ways = m×n Fundamental Counting Principle = 2×3×4 = 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 = favourableoutcometotaloutcome = 124 The probability that the meal picked for you is the one you wanted is 124124 -
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)
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Fundamental Counting Principle
number of ways =m×nFirst, list down all the categories and count the options for eachEntree:=4Side:=3Beverage:=3Dessert:=2Use the Fundamental Counting Principle and for each category multiply the number of options.number of ways = m×n Fundamental Counting Principle = 4×3×3×2 = 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)
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Fundamental Counting Principle
number of ways =m×nFirst, list down all the categories and count the options for eachEntree:=4Side:=3Dessert:=2Use the Fundamental Counting Principle and for each category multiply the number of options.number of ways = m×n Fundamental Counting Principle = 4×3×2 = 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)
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Fundamental Counting Principle
number of ways =m×nFirst, list down all the categories and count the options for eachEntree:=3Side:=3Beverage:=3Dessert:=1Use the Fundamental Counting Principle and for each category multiply the number of options.number of ways = m×n Fundamental Counting Principle = 3×3×3×1 = 27 You can have 27 different set of meals.27
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