NOTE: The word arrangement tells us that the order of the statues in the display matters.

Take the task of displaying 3 statues and break it into stages.

Stage 1: Select a statue for the first position
There are nine statues from which to choose. So, we can complete stage 1 in 9 ways

Stage 2: Select a statue for the second position
There are 8 statues remaining. So, we can complete stage 2 in 8 ways

Stage 3: Select a statue for the third position
There are 7 statues remaining. So, we can complete stage 3 in 7 ways

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus arrange three statues) in (9)(8)(7) ways (= 504 ways)

Answer: 504

Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.

RELATED VIDEO

Jess has nine different statues

They are not identical

chooses three to arrange

Arrange word will almost always be related to permutation

Permutation - The number of ways to arrange a set of items
Combination - The number of ways to combine a set of items

So, we have to arrange 3 out of 9 statues, which can be done in \(^9P_3\) ways = \(9*8*7\) = 504 ways

If the statues were identical, just divide the above answer by 3!

9P3 ways

i.e. 9!/(9-3)!
= 9!/6!
= 9x8x7x6!/ 6!
= 9x8x7
= 504 ways

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