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

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

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New post 02 Apr 2017, 23:39
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Question Stats:

54% (01:20) correct 46% (01:10) wrong based on 74 sessions

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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

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Re: Eight dogs are in a pen when the owner comes to walk some of them. The  [#permalink]

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New post 03 Apr 2017, 03:25
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
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Re: Eight dogs are in a pen when the owner comes to walk some of them. The  [#permalink]

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New post 06 Apr 2017, 08:32
Bunuel wrote:
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


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
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Re: Eight dogs are in a pen when the owner comes to walk some of them. The  [#permalink]

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New post 22 Feb 2018, 09:37
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Bunuel wrote:
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


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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Re: Eight dogs are in a pen when the owner comes to walk some of them. The &nbs [#permalink] 22 Feb 2018, 09:37
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