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

Question

Eight dogs are in a pen when the owner comes to walk some of them. The owner lets five dogs out of the pen one at a time. How many different variations in the line of dogs leaving the pen are possible?

A. 6,720
B. 3,360
C. 1,680
D. 560
E. 56

A. 6,720
B. 3,360
C. 1,680
D. 560
E. 56

RR88 · Answer

Option A

Total no. of Dogs = 8
No. of Dogs leaving pen = No. of Dogs in line = 5

Total variations in line formation = Total combinations of arranging 5 (out of 8) Dogs = 8*7*6*5*4 = 6,720

ScottTargetTestPrep · Answer

We are given that there are 8 dogs and the owner needs to arrange 5 of them. Since we have an “order arrangement,” order matters. So we have a permutation problem. Thus, the number of ways to arrange 5 dogs from 8 is:

8P5 = 8!/(8-5)! = 8 x 7 x 6 x 5 x 4 = 6,720

Answer: A

BrentGMATPrepNow · Answer

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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