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# Dennis's teacher gave his class a task of planting trees.

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Manager
Joined: 25 Dec 2018
Posts: 148
Location: India
GMAT 1: 490 Q47 V13
GPA: 2.86

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31 Jan 2019, 08:40
1
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:35) correct 27% (02:26) wrong based on 44 sessions

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Dennis's teacher gave his class a task of planting trees. Dennis and his 5 friends thought of planting 6 trees in a row, so they bought one sapling each. How many ways could they plan them if one friend bought Rose sapling, 2 of them bought identical Blackberry saplings, 2 bought identical tulip saplings and one bought an orchid sapling?

A. 120
B. 160
C. 180
D. 200
E. 240
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Joined: 09 Mar 2018
Posts: 1003
Location: India
Re: Dennis's teacher gave his class a task of planting trees.  [#permalink]

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31 Jan 2019, 09:35
akurathi12 wrote:
Dennis's teacher gave his class a task of planting trees. Dennis and his 5 friends thought of planting 6 trees in a row, so they bought one sapling each. How many ways could they plan them if one friend bought Rose sapling, 2 of them bought identical Blackberry saplings, 2 bought identical tulip saplings and one bought an orchid sapling?

A. 120
B. 160
C. 180
D. 200
E. 240

Do note of these

Plants can be planted in(since they are identical we will include them twice(2!))
6!/2!*2!

180

C
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Re: Dennis's teacher gave his class a task of planting trees.  [#permalink]

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04 Feb 2019, 18:58
akurathi12 wrote:
Dennis's teacher gave his class a task of planting trees. Dennis and his 5 friends thought of planting 6 trees in a row, so they bought one sapling each. How many ways could they plan them if one friend bought Rose sapling, 2 of them bought identical Blackberry saplings, 2 bought identical tulip saplings and one bought an orchid sapling?

A. 120
B. 160
C. 180
D. 200
E. 240

We can represent the trees as:

R - B - B - T - T - O

We use the indistinguishable permutations formula because of the 2 identical Blackberry saplings and the 2 identical tulip saplings. Thus, the total number of arrangements is 6!/(2! x 2!) = (6 x 5 x 4 x 3 x 2)/(2 x 2) = 6 x 5 x 3 x 2 = 180.

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Re: Dennis's teacher gave his class a task of planting trees.   [#permalink] 04 Feb 2019, 18:58
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