Eight dogs are in a pen when the owner comes to walk some of them. The

Take the task of arranging the 5 dogs in a line and break it into stages.

Stage 1: Select a dog to be 1st in the line
There are 8 dogs to choose from, so, we can complete stage 1 in 8 ways

Stage 2: Select a dog to be 2nd in the line
There are 7 remaining dogs from which to choose, so we can complete this stage in 7 ways.

Stage 3: Select a dog to be 3rd in the line
There are 6 remaining dogs from which to choose, so we can complete this stage in 6 ways.

Stage 4: Select a dog to be 4th in the line
There are 5 remaining dogs from which to choose, so we can complete this stage in 5 ways.

Stage 5: Select a dog to be 5th in the line
There are 4 remaining dogs from which to choose, so we can complete this stage in 4 ways.

By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus arrange 5 dogs in a line) in (8)(7)(6)(5)(4) ways (= 6720 ways)

Answer: A

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

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