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Probability .. Marbles

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AlexTsipkis
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Probability .. Marbles [#permalink] New post   23 Nov 2006, 04:49
Hi,

Suppose 5 marbles are placed in 5 boxes at random. Find the probability p that exactly 1 of the boxes is empty.


Could somebody solve this question with clear explantion especially in how many ways marbles are selected to place 5 marbles in 5 boxes. I thought it would be 5! ways, but it didn't work out.



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Re: Probability .. Marbles [#permalink] New post   23 Nov 2006, 07:24
Total Outcomes = 2^5 =32 -1 ( all boxes empty)
ex

consider the 5 boxes lined up, 1= marble (s) in the box, 0= no marble in the box

00000 ( not possible, since all boxes are empty)
00001 ( all 5 marbles on the last box)
00010
00100
etc..

The probability of only one become empty is 5C1=5
so P =5/31

Sorry if it's too complicated on the binary way
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Re: Probability .. Marbles [#permalink] New post   24 Nov 2006, 17:05
Why eliminate the case of no marbes in any of the boxes. Why not 5/32
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Re: Probability .. Marbles [#permalink] New post   24 Nov 2006, 22:52
The question is not clear to me. Did he post the exactly worded question?

e.g. if 5 marbles fill exactly 5 boxes, if we exchange 2 marbles in them, is it counted as the same or different?

if it is the same, i.e. it is a combination problem, then i got 1/7.

if different, i.e. it is a permutation problem, i get 12/125. this is much more complex.
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Re: Probability .. Marbles [#permalink] New post   25 Nov 2006, 18:18
5/31 but i would have done in the combinations way.

Ways to keep 5 marbles in:

5 boxes - 5C5
4 boxes - 5C4
3 boxes - 5C3
2 boxes - 5C2
1 box - 5C1


Total ways - 31
out of this our choice is 4 boxes, hence 5/31.
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Re: Probability .. Marbles [#permalink] New post   16 Jan 2007, 08:08
Why is the Total Outcomes not 5^5

5^5 because :-

For 1st Marble, there are 5 boxes
For 2nd Marble , there are 5 boxes
For 3rd Marble, there are 5 boxes
for 4th Marble , there are 5 boxes
For 5th Marble, there are 5 boxes

Hence Total Outcomes for assigning all 5 marbles to 5 boxes=5^5

Can anyone pl explain why this is not applicable here?

Thanks



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Re: Probability .. Marbles [#permalink]
16 Jan 2007, 08:08
Moderator:
yashikaaggarwal
Senior Moderator - Masters Forum
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