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| The botanic garden is planting bulbs for the spring flower https://gmatclub.com/forum/the-botanic-garden-is-planting-bulbs-for-the-spring-flower-106763.html |
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| Author: | rxs0005 [ 22 Dec 2010, 08:22 ] |
| Post subject: | The botanic garden is planting bulbs for the spring flower |
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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| Author: | Bunuel [ 22 Dec 2010, 09:10 ] |
| Post subject: | Re: Combibations PS |
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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| Author: | mailnavin1 [ 22 Dec 2010, 09:09 ] |
| Post subject: | Re: Combibations PS |
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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| Author: | GMATinsight [ 22 Dec 2015, 02:02 ] |
| Post subject: | Re: The botanic garden is planting bulbs for the spring flower |
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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| Author: | ScottTargetTestPrep [ 21 Dec 2022, 11:56 ] |
| Post subject: | Re: The botanic garden is planting bulbs for the spring flower |
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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