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# The botanic garden is planting bulbs for the spring flower

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Director
Joined: 07 Jun 2004
Posts: 612
Location: PA
The botanic garden is planting bulbs for the spring flower [#permalink]

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22 Dec 2010, 08:22
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The botanic garden is planting bulbs for the spring flower show. The head gardener is trying to decide how to place three Tulips bulbs, three Daffodil bulbs, and three Crocus bulbs along the front row. How many different arrangements can he make of these bulbs in the front row?

(A) 27
(B) 108
(C) 216
(D) 512
(E) 1,680
[Reveal] Spoiler: OA

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22 Dec 2010, 09:09
total number of bulbs is 9, hence possible arrangements is 9!

But all the 3 bulbs are 3 each, hence

$$i.e., 9!/3!3!3! = 1680 ways$$
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22 Dec 2010, 09:10
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rxs0005 wrote:
The botanic garden is planting bulbs for the spring flower show. The head gardener is trying to decide how to place three Tulips bulbs, three Daffodil bulbs, and three Crocus bulbs along the front row. How many different arrangements can he make of these bulbs in the front row?

(A) 27
(B) 108
(C) 216
(D) 512
(E) 1,680

# of ways to arrange 9 flowers out of which 3 T's are identical, 3 D's are identical and 3 C's are identical is 9!/(3!3!3!)=1,680.

Check this for more: counting-ps-106762.html#p840035

Hope it helps.
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Re: The botanic garden is planting bulbs for the spring flower [#permalink]

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19 Dec 2015, 04:52
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: The botanic garden is planting bulbs for the spring flower [#permalink]

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22 Dec 2015, 02:02
rxs0005 wrote:
The botanic garden is planting bulbs for the spring flower show. The head gardener is trying to decide how to place three Tulips bulbs, three Daffodil bulbs, and three Crocus bulbs along the front row. How many different arrangements can he make of these bulbs in the front row?

(A) 27
(B) 108
(C) 216
(D) 512
(E) 1,680

9 objects in total can be arranged in 9!
But 3 Tulip are alike so divide by 3!
and 3 Daffodil are alike so divide by 3!
and 3 Crocus are alike so divide by 3!

9!/(3!*3!*3!) = 1680

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Re: The botanic garden is planting bulbs for the spring flower   [#permalink] 22 Dec 2015, 02:02
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