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Permutation problem

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by abhirup1711 » Thu Jun 06, 2013 4:32 am
Kendra is a faculty advisor and she helps 4 student leaders, 3 faculty members and 5 administrators meet and learn about each other.She decides to invite 1 student, 1 faculty member and 1 administator to lunch every Friday. For how many Fridays can Kendra avoid having lunch with the exact same combination of student, faculty and administrator?
12
48
60
64
68

May I ask someone to help me with this?
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by Atekihcan » Thu Jun 06, 2013 4:38 am
Number of different lunch groups consisting of 1 student, 1 faculty member and 1 administrator
= (number of ways to select 1 student among 4)*(number of ways to select 1 faculty member among 3)*(number of ways to select 1 administrator among 5)
= 4*3*5
= 60

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by Brent@GMATPrepNow » Thu Jun 06, 2013 6:33 am
By the way, Atekihcan is applying a technique known as the Fundamental Counting Principle (FCP). The FCP can be used to solve MANY (perhaps at least half of all) counting questions you'll find on the GMAT, so be sure you know it.

If anyone is interested, we have a free video on the subject: https://www.gmatprepnow.com/module/gmat-counting?id=775

Cheers,
Brent

Aside: The FCP is also referred to as the "slot method"
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