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

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

by BTGModeratorVI » Mon Apr 13, 2020 3:40 pm

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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

Answer: A
Source: Veritas Prep
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Re: Five friends - Ross, Phoebe, Chandler, Joey, and Monica

by Jay@ManhattanReview » Thu Apr 16, 2020 12:53 am
BTGModeratorVI wrote: ↑
Mon Apr 13, 2020 3:40 pm
 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

Answer: A
Source: Veritas Prep
• The no. of choices Ross has = 3;
• The no. of choices Phoebe has = 1;
• The no. of choices Chandler has = 3; since Ross and Phoebe have already chosen two out of five types of pizzas, Chandler has ONLY three choices
• The no. of choices Joey has = 2;
• The no. of choice Monica has = 1

Total no. of ways = 3*1*3*2*1 = 18

The correct answer: A

Hope this helps!

-Jay
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Re: Five friends - Ross, Phoebe, Chandler, Joey, and Monica

by swerve » Thu Apr 16, 2020 1:58 pm
BTGModeratorVI wrote: ↑
Mon Apr 13, 2020 3:40 pm
 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

Answer: A
Source: Veritas Prep
Phoebe \(= 1\)
Ross \(= 3\) ways
Chandler \(= 3\) ways
Joey \(= 2\) ways
Monica \(= 1\) way
Total \(3 \cdot 3 \cdot 2 \cdot 1 \cdot 1 = 18\)
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Re: Five friends - Ross, Phoebe, Chandler, Joey, and Monica

by Scott@TargetTestPrep » Fri Apr 17, 2020 10:52 am
BTGModeratorVI wrote: ↑
Mon Apr 13, 2020 3:40 pm
 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

Answer: A
Source: Veritas Prep
Let’s 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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