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Five friends - Ross, Phoebe, Chandler, Joey, and Monica - decide to ha
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27 Mar 2017, 04:00

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Difficulty:

65% (hard)

Question Stats:

56% (01:43) correct 44% (01:38) wrong based on 150 sessions

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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?

Re: Five friends - Ross, Phoebe, Chandler, Joey, and Monica - decide to ha
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27 Mar 2017, 08:35

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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)

Re: Five friends - Ross, Phoebe, Chandler, Joey, and Monica - decide to ha
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29 Mar 2017, 10:04

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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
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22 Aug 2018, 13:21

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?