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The botanic garden is planting bulbs for the spring flower

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rxs0005
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The botanic garden is planting bulbs for the spring flower [#permalink] New post  22 Dec 2010, 07:22
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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
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Bunuel
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Re: Combibations PS [#permalink] New post  22 Dec 2010, 08:10
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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.

Answer: E.

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

Hope it helps.
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Re: Combibations PS [#permalink] New post  22 Dec 2010, 08:09
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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Re: The botanic garden is planting bulbs for the spring flower [#permalink] New post  22 Dec 2015, 01:02
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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


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

Answer : Option E
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Re: The botanic garden is planting bulbs for the spring flower [#permalink] New post  21 Dec 2022, 10:56
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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


Since we are not told otherwise, we can assume the three tulips, three daffodils, and crocuses are identical. Thus, the total number of arrangments is:

9!/(3! x 3! x 3!) = (9 x 8 x 7 x 6 x 5 x 4)/(3 x 2 x 3 x 2) = 8 x 7 x 6 x 5 = 1,680
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Re: The botanic garden is planting bulbs for the spring flower [#permalink]
21 Dec 2022, 10:56
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