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

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Bunuel
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Eight dogs are in a pen when the owner comes to walk some of them. The [#permalink] New post   03 Apr 2017, 00:33
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Eight dogs are in a pen when the owner comes to walk some of them. The owner lets four dogs out of the pen one at a time. How many different variations in the line of dogs leaving the pen are possible?

A. 3,360
B. 1,680
C. 540
D. 60
E. 24
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B
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Re: Eight dogs are in a pen when the owner comes to walk some of them. The [#permalink] New post   03 Apr 2017, 03:36
IMO B
You need to use permutation in this case
8!/(8-4)!=1680
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Re: Eight dogs are in a pen when the owner comes to walk some of them. The [#permalink] New post   06 Apr 2017, 09:33
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Bunuel wrote:
Eight dogs are in a pen when the owner comes to walk some of them. The owner lets four dogs out of the pen one at a time. How many different variations in the line of dogs leaving the pen are possible?

A. 3,360
B. 1,680
C. 540
D. 60
E. 24


We are given that there are 8 dogs and the owner needs to arrange 4 of them. Since we have an “order arrangement,” order matters. So we have a permutation problem. Thus, the number of ways to arrange 4 dogs from 8 is:

8P4 = 8!/(8-4)! = 8 x 7 x 6 x 5 = 1,680

Answer: B
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Re: Eight dogs are in a pen when the owner comes to walk some of them. The [#permalink] New post   18 May 2017, 03:55
Bunuel wrote:
Eight dogs are in a pen when the owner comes to walk some of them. The owner lets four dogs out of the pen one at a time. How many different variations in the line of dogs leaving the pen are possible?

A. 3,360
B. 1,680
C. 540
D. 60
E. 24


First we should make a group of 4 dogs which will be let out. Then we will find how many arrangements of such leaving will be possible.

So no. of ways in which a group of 4 dogs can be formed = \(8C4\) = (8*7*6*5)/(4*3*2*1) = 70

The total no. of ways in which the line of dogs leaving the pen are possible = 70 X 4! = 70*4*3*2= 1680


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Re: Eight dogs are in a pen when the owner comes to walk some of them. The [#permalink] New post   26 Nov 2018, 12:33
No of ways to arrange 4 from 8
8P4 = 1680 (B)
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Re: Eight dogs are in a pen when the owner comes to walk some of them. The [#permalink]
26 Nov 2018, 12:33
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