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Five friends - Ross, Phoebe, Chandler, Joey and Monica -

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AAPL: Moderator; Posts: 2651; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Fri Dec 21, 2018 3:01 am

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Veritas Prep

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

OA A

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Source: Beat The GMAT — Problem Solving | Fri Dec 21, 2018 3:01 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Dec 21, 2018 3:37 am

AAPL wrote:Veritas Prep

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

Number of options for Phoebe = 1. (Must be Margherita.)
Number of options for Ross = 3. (Of the 4 remaining pizzas, any but Hawaiian.)
Number of options for Chandler = 3. (Any of the 3 remaining pizzas.)
Number of options for Joey = 2. (Either of the 2 remaining pizzas.)
Number of options for Monica = 1. (Only 1 pizza left.)
To combine these options, we multiply:
1*3*3*2*1 = 18.

The correct answer is A.

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by Brent@GMATPrepNow » Fri Dec 21, 2018 6:57 am

AAPL wrote:Veritas Prep

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
OA A

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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8157; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Feb 24, 2019 5:35 am

AAPL wrote:Veritas Prep

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

OA A

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 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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Founder and CEO
[email protected]

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