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4. a) 15 b) 225 c) 375 5. a) 338 b) 676 c) The heart is on the bottom and the black card on top, or the black card on the bottom and the heart on top: 13 26+26 13 = 676. The heart is chosen in 13 ways, the black card in 26 ways, and the card on the bottom in 2 ways: 13.26-2 = 676. d) Because in part b, the order in which the cards are drawn matters. 6. a) 72 b) 102 c) 2, 3 and 5 7. a) 128 b) 64 c) 63 d) Why are the answers different in parts a and b? Exercise 6 In ice cream kiosks, you can choose a cone, flavor, and toppings for an ice cream dish. a) The first kiosk has three cones, six flavors, and four different toppings. How many different ice cream dishes can be made? b) The second kiosk only has a total of 30 different ice cream dishes. How many different ice cream dishes can a customer choose if they can go to either kiosk? c) Can you determine the number of cones, flavors, and toppings in the second kiosk? The order of these cannot be known, but the quantities are unique integers.

4. a) 15 b) 225 c) 375 5. a) 338 b) 676 c) The heart is on the bottom and the black card on top, or the black card on the bottom and the heart on top: 13 26+26 13 = 676. The heart is chosen in 13 ways, the black card in 26 ways, and the card on the bottom in 2 ways: 13.26-2 = 676. d) Because in part b, the order in which the cards are drawn matters. 6. a) 72 b) 102 c) 2, 3 and 5 7. a) 128 b) 64 c) 63 d) Why are the answers different in parts a and b? Exercise 6 In ice cream kiosks, you can choose a cone, flavor, and toppings for an ice cream dish. a) The first kiosk has three cones, six flavors, and four different toppings. How many different ice cream dishes can be made? b) The second kiosk only has a total of 30 different ice cream dishes. How many different ice cream dishes can a customer choose if they can go to either kiosk? c) Can you determine the number of cones, flavors, and toppings in the second kiosk? The order of these cannot be known, but the quantities are unique integers.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 37E
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Product rule combinatorics. Please solve all parts correctly and handwritten. Answers attached
4. a) 15 b) 225 c) 375 5. a) 338 b) 676 c) The heart is on the bottom and the black card on top, or the black card on the bottom and the heart on top: 13 26+26 13 = 676. The heart is chosen in 13 ways, the black card in 26 ways, and the card on the bottom in 2 ways: 13.26-2 = 676. d) Because in part b, the order in which the cards are drawn matters. 6. a) 72 b) 102 c) 2, 3 and 5 7. a) 128 b) 64 c) 63
Transcribed Image Text:4. a) 15 b) 225 c) 375 5. a) 338 b) 676 c) The heart is on the bottom and the black card on top, or the black card on the bottom and the heart on top: 13 26+26 13 = 676. The heart is chosen in 13 ways, the black card in 26 ways, and the card on the bottom in 2 ways: 13.26-2 = 676. d) Because in part b, the order in which the cards are drawn matters. 6. a) 72 b) 102 c) 2, 3 and 5 7. a) 128 b) 64 c) 63
d) Why are the answers different in parts a and b? Exercise 6 In ice cream kiosks, you can choose a cone, flavor, and toppings for an ice cream dish. a) The first kiosk has three cones, six flavors, and four different toppings. How many different ice cream dishes can be made? b) The second kiosk only has a total of 30 different ice cream dishes. How many different ice cream dishes can a customer choose if they can go to either kiosk? c) Can you determine the number of cones, flavors, and toppings in the second kiosk? The order of these cannot be known, but the quantities are unique integers.
Transcribed Image Text:d) Why are the answers different in parts a and b? Exercise 6 In ice cream kiosks, you can choose a cone, flavor, and toppings for an ice cream dish. a) The first kiosk has three cones, six flavors, and four different toppings. How many different ice cream dishes can be made? b) The second kiosk only has a total of 30 different ice cream dishes. How many different ice cream dishes can a customer choose if they can go to either kiosk? c) Can you determine the number of cones, flavors, and toppings in the second kiosk? The order of these cannot be known, but the quantities are unique integers.
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