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27 Mar 2017, 04:00
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
62% (01:45) correct
38%
(01:37)
wrong
based on 534
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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
A. 18
B. 24
C. 48
D. 96
E. 120
27 Mar 2017, 08:35
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Bunuel
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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General Discussion
29 Mar 2017, 10:04
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Bunuel
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
