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

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Joined: 25 Dec 2018
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Dennis's teacher gave his class a task of planting trees.  [#permalink]

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New post 31 Jan 2019, 09:40
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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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Re: Dennis's teacher gave his class a task of planting trees.  [#permalink]

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New post 31 Jan 2019, 10:35
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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New post 04 Feb 2019, 19:58
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.

Answer: C
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Re: Dennis's teacher gave his class a task of planting trees.   [#permalink] 04 Feb 2019, 19:58
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Dennis's teacher gave his class a task of planting trees.

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