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

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

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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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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

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: http://www.gmatprepnow.com/module/gmat-counting/video/775

You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat-counting/video/776

Then you can try solving the following questions:

EASY
- http://www.beatthegmat.com/what-should-be-the-answer-t267256.html
- http://www.beatthegmat.com/counting-problem-company-recruitment-t244302.html
- http://www.beatthegmat.com/picking-a-5-digit-code-with-an-odd-middle-digit-t273110.html
- http://www.beatthegmat.com/permutation-combination-simple-one-t257412.html
- http://www.beatthegmat.com/simple-one-t270061.html


MEDIUM
- http://www.beatthegmat.com/combinatorics-solution-explanation-t273194.html
- http://www.beatthegmat.com/arabian-horses-good-one-t150703.html
- http://www.beatthegmat.com/sub-sets-probability-t273337.html
- http://www.beatthegmat.com/combinatorics-problem-t273180.html
- http://www.beatthegmat.com/digits-numbers-t270127.html
- http://www.beatthegmat.com/doubt-on-separator-method-t271047.html
- http://www.beatthegmat.com/combinatorics-problem-t267079.html


DIFFICULT
- http://www.beatthegmat.com/wonderful-p-c-ques-t271001.html
- http://www.beatthegmat.com/permutation-and-combination-t273915.html
- http://www.beatthegmat.com/permutation-t122873.html
- http://www.beatthegmat.com/no-two-ladies-sit-together-t275661.html
- http://www.beatthegmat.com/combinations-t123249.html


Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
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GMAT/MBA Expert

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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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Post
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

_________________

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



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