Problem Solving

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

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

theCodeToGMAT wrote:Editing

what does this mean?

parveen110 wrote:

theCodeToGMAT wrote:Editing

what does this mean?

I was correcting my post. I got confused between similar posts by you.