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Permutation and combination

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Permutation and combination

by parveen110 » Mon Jan 20, 2014 11:44 pm
There are 5 identical boxes and 7 identical balls.All the balls are to be distributed in the 5 boxes placed in a row so that any box can recieve any number of balls. Then in how many ways can all these balls be distributed into these boxes?

a.12
b.13
c.16
d.255

OA: B
Last edited by parveen110 on Fri Jan 24, 2014 9:26 am, edited 1 time in total.
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by theCodeToGMAT » Tue Jan 21, 2014 1:09 am
Since, boxes and balls are identical..

So possible orientations:

No 0
=> 7 balls 5 boxes
Now distribute one ball each .. so we are now left with 2 balls and 5 boxes
=> Possible orientations = 1 1 or 0 2
So, 2 ways

One 0
=> 7 balls 4 boxes
Now distribute one ball each .. so we are now left with 3 balls and 4 boxes
=> Possible orientations = 1 1 1 or 1 2 or 0 3
So, 3 Ways

Two 0
=> 7 balls 3 boxes
Now distribute one ball each .. so we are now left with 4 balls and 3 boxes
=> Possible orientations = 1 1 2 or 1 3 or 0 4 or 2 2
So, 4 Ways

Three 0
=> 7 balls 2 boxes
Now distribute one ball each .. so we are now left with 5 balls and 2 boxes
=> Possible orientations = 2 3 or 0 5 or 1 4
So, 3 Ways

four 0
=> 7 balls 1 boxes
So, 1 way

Total Ways = 2+3+4+3+1 = 13 ways
Last edited by theCodeToGMAT on Tue Jan 21, 2014 2:17 am, edited 1 time in total.
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by parveen110 » Tue Jan 21, 2014 1:55 am
theCodeToGMAT wrote:Editing
what does this mean?
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by theCodeToGMAT » Tue Jan 21, 2014 2:17 am
parveen110 wrote:
theCodeToGMAT wrote:Editing
what does this mean?
I was correcting my post. I got confused between similar posts by you.
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