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A principal has four different trophies available for displa
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03 Mar 2019, 03:36
03 Mar 2019, 03:36
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A principal has four different trophies available for display in his two display cases. If only one trophy can fit in each display case, how many distinct ways are there to display two of the trophies in the cases at any given time?
A. 16
B. 12
C. 9
D. 8
E. 6
A. 16
B. 12
C. 9
D. 8
E. 6
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A principal has four different trophies available for displa
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07 Mar 2019, 09:53
07 Mar 2019, 09:53
Carcass wrote:
A principal has four different trophies available for display in his two display cases. If only one trophy can fit in each display case, how many distinct ways are there to display two of the trophies in the cases at any given time?
A. 16
B. 12
C. 9
D. 8
E. 6
A. 16
B. 12
C. 9
D. 8
E. 6
Take the task of displaying two of the trophies and break it into stages.
Let's call the two trophy cases Trophy Case A and Trophy Case B
Stage 1: Select a trophy to display in Trophy Case A
There are 4 trophies to choose from.
So, we can complete stage 1 in 4 ways
Stage 2: Select a trophy to display in Trophy Case B
There are 3 REMAINING trophies to choose from.
So, we can complete stage 2 in 3 ways
By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus display 2 trophies) in (4)(3) ways (= 12 ways)
Answer: B
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
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A principal has four different trophies available for displa [#permalink]
07 Mar 2019, 09:53
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