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# A farmer is planting a row consisting of 4 unique apple trees and 4 un

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Math Expert
Joined: 02 Sep 2009
Posts: 43889
A farmer is planting a row consisting of 4 unique apple trees and 4 un [#permalink]

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08 Apr 2016, 01:42
3
KUDOS
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Difficulty:

65% (hard)

Question Stats:

58% (01:19) correct 42% (01:39) wrong based on 106 sessions

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A farmer is planting a row consisting of 4 unique apple trees and 4 unique orange trees. How many ways are there for the farmer to plant the trees such that no apple tree is adjacent to another apple tree and no orange tree is adjacent to another orange tree?

A. 512
B. 576
C. 1,024
D. 1,152
E. 10,080
[Reveal] Spoiler: OA

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Manager
Joined: 09 Jul 2013
Posts: 110
Re: A farmer is planting a row consisting of 4 unique apple trees and 4 un [#permalink]

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08 Apr 2016, 06:36
Since no trees of the same type can be adjacent to one another, there must be one apple tree between each pair of orange trees, and one orange tree between each pair of apple trees. In other words, the trees must alternate. This can be done in two ways:
1. AOAOAOAO
2. OAOAOAOA

The two types of trees have 4 unique trees each, so the 4 trees of each type can be arranged in 4! ways.
The orange trees can be arranged in 4! ways, and the apple trees can be arranged in 4! ways.

Total number of arrangements = 4!*4!*2 = 24*24*2 = 1152

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Dave de Koos

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Joined: 24 Nov 2015
Posts: 584
Location: United States (LA)
Re: A farmer is planting a row consisting of 4 unique apple trees and 4 un [#permalink]

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18 Apr 2016, 11:24
1
KUDOS
2 possible arrangements are possible
AOAOAOAO
OAOAOAOA
2 unique type of trees are present consisting of 4 trees each
4 apple trees can be arranged in 4! ways
4 orange trees can be arranged in 4! ways
as 2 arrangements are possible
total arrangements = 2 *4! * 4! = 1152
Manager
Joined: 20 Mar 2015
Posts: 62
Re: A farmer is planting a row consisting of 4 unique apple trees and 4 un [#permalink]

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21 Jul 2016, 23:21
Bunuel wrote:
A farmer is planting a row consisting of 4 unique apple trees and 4 unique orange trees. How many ways are there for the farmer to plant the trees such that no apple tree is adjacent to another apple tree and no orange tree is adjacent to another orange tree?

A. 512
B. 576
C. 1,024
D. 1,152
E. 10,080

A row consisting of 8 trees is what we need where no two same fruit is placed one after another. Either orange first and then apple or apple first and then orange.

This is our row : $$8*4*3*3*2*2*1*1$$ = 1152
Non-Human User
Joined: 09 Sep 2013
Posts: 13791
Re: A farmer is planting a row consisting of 4 unique apple trees and 4 un [#permalink]

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13 Jan 2018, 19:55
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A farmer is planting a row consisting of 4 unique apple trees and 4 un   [#permalink] 13 Jan 2018, 19:55
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