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# There are five different boxes with building materials. In

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Manager
Joined: 24 Jun 2003
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There are five different boxes with building materials. In [#permalink]  11 Aug 2003, 06:54
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There are five different boxes with building materials. In how many ways those boxes could be distributed between six stories of a building if exactly one of the boxes should be on the fifth floor and another four could be placesd at any other stories?
SVP
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[#permalink]  11 Aug 2003, 08:55
I assume that several boxes could be at any store. One store is fixed; one box is fixed.

Any other box (4) could placed in any other store (5)

So, it is 5^4=625
Manager
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[#permalink]  14 Aug 2003, 23:42
stolyar wrote:
I assume that several boxes could be at any store. One store is fixed; one box is fixed.

Any other box (4) could placed in any other store (5)

So, it is 5^4=625

Hey Stolyar, shouldn't it be 5! = 120 since one box can only be assigned to one floor, in the same way as a box is assigned to the fifth floor !
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[#permalink]  15 Aug 2003, 00:27
you wrongly prohibit repetitions.

the question stem: exactly one of the boxes should be on the fifth floor and other four could be placed at any other stories?

No conditon that exactly one box should lie on a floor, considering the other 4 boxes. They could lie together on each floor, for example.

Moreover, 5! means five boxes on five places, but you have 5 boxes and 6 floors.

But I also made a mistake: exactly one of the boxes should be on the fifth floor -- we should take 1 out of 5; 5C1=5. The other four give 5^4 ways to be placed.

Total 5*5^4=5^5
Manager
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[#permalink]  15 Aug 2003, 01:17
stolyar wrote:
you wrongly prohibit repetitions.

the question stem: exactly one of the boxes should be on the fifth floor and other four could be placed at any other stories?

No conditon that exactly one box should lie on a floor, considering the other 4 boxes. They could lie together on each floor, for example.

Moreover, 5! means five boxes on five places, but you have 5 boxes and 6 floors.

But I also made a mistake: exactly one of the boxes should be on the fifth floor -- we should take 1 out of 5; 5C1=5. The other four give 5^4 ways to be placed.

Total 5*5^4=5^5

Agree with you.... my mistake
[#permalink] 15 Aug 2003, 01:17
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