Five friends - Ross, Phoebe, Chandler, Joey, and Monica - decide to have lunch at a pizzeria. Five types of individual pizza are available: Hawaiian, Supreme, Veggie, Pepperoni, and Margherita. If Ross refuses to eat Hawaiian, Phoebe will only eat Margherita, and no two friends will eat the same type of pizza, in how many ways can they order lunch?
A. 18
B. 24
C. 48
D. 96
E. 120
Answer: A
Source: Veritas Prep
Five friends - Ross, Phoebe, Chandler, Joey, and Monica
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Types of pizza: Hawaiian, Supreme, Veggie, Pepperoni, and MargheritaBTGModeratorVI wrote: ↑Tue Jul 07, 2020 6:16 amFive friends - Ross, Phoebe, Chandler, Joey, and Monica - decide to have lunch at a pizzeria. Five types of individual pizza are available: Hawaiian, Supreme, Veggie, Pepperoni, and Margherita. If Ross refuses to eat Hawaiian, Phoebe will only eat Margherita, and no two friends will eat the same type of pizza, in how many ways can they order lunch?
A. 18
B. 24
C. 48
D. 96
E. 120
Answer: A
Source: Veritas Prep
Friends: Ross, Phoebe, Chandler, Joey, and Monica
• Phoebe --> Margherita;
• Ross --> One out of Supreme, Veggie, and Pepperoni --> 3 choices
• Chandler, Joey, and Monica --> To choose any 3 pizza out of 3 pizza --> 3*2*1 = 6 choices
# of many ways they can order lunch = 3*6 = 18
Correct answer: A
Hope this helps!
-Jay
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Take the task of feeding the 5 friends and break it into stages.BTGModeratorVI wrote: ↑Tue Jul 07, 2020 6:16 amFive friends - Ross, Phoebe, Chandler, Joey, and Monica - decide to have lunch at a pizzeria. Five types of individual pizza are available: Hawaiian, Supreme, Veggie, Pepperoni, and Margherita. If Ross refuses to eat Hawaiian, Phoebe will only eat Margherita, and no two friends will eat the same type of pizza, in how many ways can they order lunch?
A. 18
B. 24
C. 48
D. 96
E. 120
Answer: A
Source: Veritas Prep
We’ll begin with the most restrictive stage(s).
Stage 1: Select a pizza for Phoebe
Since Phoebe will only eat Margherita pizza, there's only 1 pizza we can serve her.
So, we can complete stage 1 in 1 way
Stage 2: Select a pizza for Ross
There are 4 pizzas remaining, but 1 of them is Hawaiian (which Ross refuses to eat).
So, there are only 3 pizzas we can serve Ross
We can complete stage 2 in 3 ways
Stage 3: Select a pizza for Chandler
There are 3 pizzas remaining, so we can complete stage 3 in 3 ways
Stage 4: Select a pizza for Joey
There are 2 pizzas remaining, so we can complete stage 4 in 2 ways
Stage 5: Select a pizza for Monica
There's only 1 pizza remaining, so we can complete stage 5 in 1 way
By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus feed these "friends") in (1)(3)(3)(2)(1) ways (= 18 ways)
Answer: A
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Solution:BTGModeratorVI wrote: ↑Tue Jul 07, 2020 6:16 amFive friends - Ross, Phoebe, Chandler, Joey, and Monica - decide to have lunch at a pizzeria. Five types of individual pizza are available: Hawaiian, Supreme, Veggie, Pepperoni, and Margherita. If Ross refuses to eat Hawaiian, Phoebe will only eat Margherita, and no two friends will eat the same type of pizza, in how many ways can they order lunch?
A. 18
B. 24
C. 48
D. 96
E. 120
Answer: A
Let’s start with Ross. Since Ross will not eat Hawaiian and he can’t choose Margherita (since Phoebe must eat Margherita), the number of ways in which he can select his pizza is 3. Since Phoebe will only eat Margherita, she can select her pizza in 1 way.
Finally, since no two friends will eat the same type of pizza, the remaining three friends can select their pizza in 3! = 6 ways.
Thus, the group can select pizza in 3 x 1 x 6 = 18 ways.
Answer: A
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