For dinner at a restaurant, there are x + 1 choices of appetizers, y + 1 main courses, and z choices...
For dinner at a restaurant, there are x + 1 choices of appetizers, y + 1 main courses, and z choices of dessert. How many total possible choices are there if you choose 1 appetizer, 1 main course, and 1 dessert for your meal?
Answer/Solution
xyz+xz+yz+z
Steps/Work
x +1 appetizers,
y + 1 main courses,
z dessert
Required: 1 appetizer, 1 main course, and 1 dessert
Number of ways possible = (x+1)C1*(y+1)C1*zC1 {NC1 = N! / (N-1)!*1! = N}
Hence, number of ways = (x+1)(y+1)z = (yz+z)(x+1)=xyz+xz+yz+z
Correct Option: C
y + 1 main courses,
z dessert
Required: 1 appetizer, 1 main course, and 1 dessert
Number of ways possible = (x+1)C1*(y+1)C1*zC1 {NC1 = N! / (N-1)!*1! = N}
Hence, number of ways = (x+1)(y+1)z = (yz+z)(x+1)=xyz+xz+yz+z
Correct Option: C