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Five friends - Ross, Phoebe, Chandler, Joey, and Monica - decide to ha

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Five friends - Ross, Phoebe, Chandler, Joey, and Monica - decide to ha [#permalink]

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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
[Reveal] Spoiler: OA

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Re: Five friends - Ross, Phoebe, Chandler, Joey, and Monica - decide to ha [#permalink]

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Bunuel wrote:
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


Take the task of feeding the 5 friends and break it into stages.

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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Re: Five friends - Ross, Phoebe, Chandler, Joey, and Monica - decide to ha [#permalink]

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New post 29 Mar 2017, 09:04
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Bunuel wrote:
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


We can start with Ross. Since Ross will not eat Hawaiian and he can’t choose Margherita (since Phoebe must eat Margherita), the number of ways he can select his pizza is 3. Since Phoebe will only eat Margarita, 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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Re: Five friends - Ross, Phoebe, Chandler, Joey, and Monica - decide to ha   [#permalink] 29 Mar 2017, 09:04
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