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A particular natural history museum has three rooms

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A particular natural history museum has three rooms where fo [#permalink] New post   09 Apr 2019, 02:02
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A particular natural history museum has three rooms where fossilized dinosaur skeletons are displayed. Nine dinosaur skeletons have recently been donated to the museum. If each room will have exactly one of these skeletons added to its exhibits, how many ways are there to arrange the new skeletons?

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Re: A particular natural history museum has three rooms where fo [#permalink] New post   21 Apr 2019, 04:50
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This is a simple permutation problem.

There are 3 rooms and 9 skeletons. Each room should have a distinct skeleton so the number of possibilities are:
9*8*7 = 504
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A particular natural history museum has three rooms [#permalink] New post   12 Sep 2020, 22:47
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A particular natural history museum has three rooms where fossilized dinosaur skeletons are displayed. Nine dinosaur skeletons have recently been donated to the museum. If each room will have exactly one of these skeletons added to its exhibits, how many ways are there to arrange the new skeletons?


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Re: A particular natural history museum has three rooms [#permalink] New post   12 Sep 2020, 23:03
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total ways to arrange 9*8*7= 504
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Re: A particular natural history museum has three rooms [#permalink] New post   12 Sep 2020, 23:20
why not 9c3= 84 ways
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Re: A particular natural history museum has three rooms [#permalink] New post   13 Sep 2020, 02:02
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Basic principle of counting method

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Re: A particular natural history museum has three rooms [#permalink] New post   10 Nov 2020, 03:49
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gajala wrote:
why not 9c3= 84 ways


I also used to struggle with when to just write out ___ X ___ X ___ and when to use the formula. In this case, consider what the formula means "9 choose 3" But we are not really choosing 3. We are choosing 1 per room, or better said, we are choosing any of them for a room and then any of the left ones and then a final time. Perhaps someone else can give an example of this same question reworded so that the formula would be needed? Perhaps if we had 9 fossils, one display room and this one room was going to display 3 fossils at the same time?
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Re: A particular natural history museum has three rooms [#permalink] New post   01 Feb 2021, 18:59
If the question was to just select 3, then one could use 9C3 but since this can be arranged differently in the three different rooms, it is 9P3 = 504
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