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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: 46303
A farmer is planting a row consisting of 4 unique apple trees and 4 un [#permalink]

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08 Apr 2016, 02:42
3
3
00:00

Difficulty:

55% (hard)

Question Stats:

57% (01:16) correct 43% (01:24) wrong based on 161 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

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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, 07:36
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

Answer: D
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Dave de Koos
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Joined: 24 Nov 2015
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Re: A farmer is planting a row consisting of 4 unique apple trees and 4 un [#permalink]

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18 Apr 2016, 12:24
1
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
correct answer option D
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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22 Jul 2016, 00:21
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
Intern
Joined: 18 Jun 2017
Posts: 6
Re: A farmer is planting a row consisting of 4 unique apple trees and 4 un [#permalink]

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24 Feb 2018, 07:46
Let the unique Apple trees be A1, A2, A3 and A4
Similary, unique Orange Trees be O1,O2,O3 and O4

Condition: No Apple or orange trees should be adjacent to each other.

Two arrangements are possible:-

Case1:

_A1_A2_A3_A4 (_ represents orange trees)

Apple trees can arrange themselves in 4! way since all are unique and order matters.
Similarly, Orange trees can arrange in 4! ways.

number of arrangements: 4! * 4! = 576

Case2:

A1_A2_A3_A4_

number of arrangements: 4! * 4! = 576

Total number of arrangements : Case 1 + Case 2 = 576 *2 = 1152 (Answer)
Manager
Joined: 08 Sep 2016
Posts: 107
A farmer is planting a row consisting of 4 unique apple trees and 4 un [#permalink]

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21 Apr 2018, 08:18
There are 2 ways to arrange the trees.
1) AOAOAOAO
2) OAOAOAOA

For the first arrangement, the multiplication sequence will be: 4*4*3*3*2*2*1*1. 4 apples can be placed in the first slot. 4 oranges in the second slot. 3 apples in the 3rd slot. 3 oranges in the 4th slot...etc. This arrangement will equal 576.

The second arrangement will be similar to the first arrangement, but you will consider oranges being placed in the first slot. This arrangement will also equal 576.

576+576 = 1152.

Answer D
A farmer is planting a row consisting of 4 unique apple trees and 4 un   [#permalink] 21 Apr 2018, 08:18
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# A farmer is planting a row consisting of 4 unique apple trees and 4 un

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